4t ESO/4.06 TRIGONOMETRIA/4.06.0 Trigonometria: teoria 4.06.0.11 el costat b és vertical? En el triangle rectangle ABC, el costat b és ?

]]>

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> Vertical

]]> Horitzontal

]]> Inclinat

]]> <question/> 4.06.0.12 el costat c és horitzontal? En el triangle rectangle ABC, el costat c és ?

]]>

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> Horitzontal

]]> Vertical

]]> Inclinat

]]> <question/> 4.06.0.21 el costat c és adjacent? En un triangle rectangle ABC, el costat c és ?

]]>

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> El costat adjacent a l'angle B

]]> El costat oposat a l'angle B

]]> La hipotenusa

]]> <question/> 4.06.0.22 el costat b és oposat? En un triangle rectangle ABC, el costat b és ?

]]>

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> El costat adjacent a l'angle B

]]> El costat oposat a l'angle B

]]> La hipotenusa

]]> <question/> 4.06.0.23 el costat a és la hipotenusa? En un triangle rectangle ABC, el costat a és ?

]]>

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> El costat adjacent a l'angle B

]]> El costat oposat a l'angle B

]]> La hipotenusa

]]> <question/> 4.06.0.31 Pitàgores: trobar a En un triangle d'hipotenusa a, i de catets, b i c, com es calcula la hipotenusa a a partir dels catets b i c?

]]> És el teorema de Pitàgores

]]> 1.0000000 0.3333333 0 0 a=b2+c2]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msqrt><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></msqrt></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.32 Pitàgores: trobar b En un triangle d'hipotenusa a, i de catets, b i c,

com es calcula el costat b a partir del catet c i de la hipotenusa a?

]]> És el teorema de Pitàgores

]]> 1.0000000 0.3333333 0 0 b=a2-c2]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>c</mi><mn>2</mn></msup></msqrt></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.32 Pitàgores: trobar c En un triangle d'hipotenusa a, i de catets, b i c,

com es calcula el costat c a partir del catet b i de la hipotenusa a?

]]> És el teorema de Pitàgores

]]> 1.0000000 0.3333333 0 0 c=a2-b2]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><msqrt><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></msqrt></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.41 Deduir 3r angle B d'un triangle rectangle En un triangle rectangle, com es calcula l'angle B en funció de l'angle C?

]]> B=90º-C

]]> 1.0000000 0.3333333 0 0 B=90°-C]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mn>90</mn><mo>°</mo><mo>-</mo><mi>C</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.42 Deduir 3r angle C d'un triangle rectangle En un triangle rectangle, com es calcula l'angle C en funció de l'angle B?

]]> C=90º-B

]]> 1.0000000 0.3333333 0 0 C=90°-B]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>90</mn><mo>°</mo><mo>-</mo><mi>B</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.51 Expressió del sinus En un triangle rectangle, de catets b i c i d'hipotenusa a, escriu l'expressió de sinB en funció de a, b i c.

]]> sinB = b/a

]]> 1.0000000 0.3333333 0 0 sinB=ba]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mi>B</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.52 Expressió del cosinus En un triangle rectangle, de catets b i c i d'hipotenusa a, escriu l'expressió de cosB en funció de a, b i c.

]]> cosB = c/a

]]> 1.0000000 0.3333333 0 0 cosB=ca]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cos</mi><mi>B</mi><mo>=</mo><mfrac><mi>c</mi><mi>a</mi></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.53 Expressió de la tangent En un triangle rectangle, de catets b i c i d'hipotenusa a, escriu l'expressió de tgB en funció de a, b i c.

]]> tgB = b/c

]]> 1.0000000 0.3333333 0 0 tgB=bc]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tg</mi><mi>B</mi><mo>=</mo><mfrac><mi>b</mi><mi>c</mi></mfrac></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 4.06.0.55 Escollir raó en funció d'enunciat b i c En un triangle rectangle, si vols calcular c i a l'enunciat et donen b, cal utilitzar l'expressió de:

]]> tgB=b/c

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4.06.0.56 Escollir raó en funció d'enunciat c i a En un triangle rectangle, si vols calcular a i a l'enunciat et donen c, cal utilitzar l'expressió de:

]]> cosB=c/a

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4.06.0.57 Escollir raó en funció d'enunciat b i a En un triangle rectangle, si vols calcular a i a l'enunciat et donen b, cal utilitzar l'expressió de:

]]> sinB=b/a

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4.06.0.58 Escollir raó en funció d'enunciat a i b En un triangle rectangle, si vols calcular b i a l'enunciat et donen a, cal utilitzar l'expressió de:

]]> sinB= b/a

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4.06.0.59 Escollir raó en funció d'enunciat a i c En un triangle rectangle, si vols calcular c i a l'enunciat et donen a, cal utilitzar l'expressió de:

]]> cosB= c/a

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4.06.0.60 Escollir raó en funció d'enunciat c i b En un triangle rectangle, si vols calcular b i a l'enunciat et donen c, cal utilitzar l'expressió de:

]]> tgB= b/c

]]> 1.0000000 0.3333333 0 true true abc La teva resposta és correcta.

]]> La teva resposta és parcialment correcta.

]]> La teva resposta és incorrecta.

]]> sin B

]]> cos B

]]> tg B

]]> <question/> 4t ESO/4.06 TRIGONOMETRIA/4.06.1 Angles i triangles/4.06.1.1 Mesura d'angles 4.06.1.1.10 TEORIA: MESURA D'ANGLES

Mesura d'angles

Radiants

1 radiant és l'angle que correspon a un arc de longitud igual al radi.

Graus

Si es divideix la circumferència en 360 parts iguals, l'angle corresponent és 1 grau, que es pot subdividir en minuts i segons.

Conversió:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8594;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»d«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»20«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#215;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»§#960;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»r«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»d«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«mrow»«mn mathvariant=¨bold¨»180«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»d«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8594;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»d«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»n«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#215;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mn mathvariant=¨bold¨»180«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«mrow»«mi mathvariant=¨bold¨»§#960;«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»r«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»d«/mi»«mi mathvariant=¨bold¨»i«/mi»«mi mathvariant=¨bold¨»a«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»s«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Calculadora:

El nombre pi s'introdueix amb shift+EXP

Per convertir de sexagesimal a decimal:

3º15'20'' s'introdueix amb 3 15 20

Per transformar de decimal a sexagesimal: shift+

]]> 0.0000000 0.0000000 0 4.06.1.1.11Q Conversió Fes les conversions següents:

a) #g1 º: de graus a radiants

b) #r1 radiants: de radiants a graus

Format de la resposta:

a) fracció de π

b) arrodonida als centèsims i sense unitats

]]> 1.0000000 0.5000000 0 0 a)=#sol1b)=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>351</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mo>(</mo><mn>111</mn><mo>,</mo><mn>626</mn><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>g1</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g2</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>r2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>g2</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>,</mo><mfrac><mrow><mn>29</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>,</mo><mi>g2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.85</mn><mo>,</mo><mn>163.29</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>29</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>163.29</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Fes servir els dos factors de conversió:

de graus a radiants: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»§#960;«/mi»«mn mathvariant=¨bold¨»180«/mn»«/mfrac»«/mstyle»«/math»
de radiants a graus: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#007F00¨»«mn mathvariant=¨bold¨»180«/mn»«mi mathvariant=¨bold¨»§#960;«/mi»«/mfrac»«/mstyle»«/math»

]]> 4.06.1.1.21 Operacions en sexagesimal Efectua:

Si un resultat és zero, cal escriure'l

#s_11 + #s_12 =	{#1}º {#2}' {#3}''
#r_21 - #r_22	{#4}º {#5}' {#6}''
#m_31 · #m_32	{#7}º {#8}' {#9}''
#d_41 :#m_42	{#10}º {#11}' {#12}'' residu: {#13}''

]]> 13.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>21</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>59</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_13</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>59</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_11</mi><mo>=</mo><mi>a_11</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mi>a_12</mi><csymbol definitionURL="http://.../units/minute/angular">&apos;</csymbol><mi>a_13</mi><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_44</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>294</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_45</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_46</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Amb la calculadora no et pots equivocar.

]]> 4.06.1.1.50 TEORIA SUMA ANGLES TRIANGLE Suma dels angles d'un triangle

1. Triangle no rectangle: Com que els tres angles sumen 180º, si en sabem dos podem calcular el tercer:

B = 180º - A - C; A = 180º - B - C; C = 180º - A - B

2. Triangle rectangle: Com que l'angle A sempre fa 90º i la suma dels 3 angles és 180º:

B = 90º - C i C = 90º - B

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d/4J/V+sFfk/8Gf+Tnf+Cm3/AGeh8N//AF27/wAE/q/T/Db/AHTxF/7IbDf+vC4COLGb4T/sJf8A6i4o+oKKKK6SAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAK8q+LPwS+F/wAcNFsNF+JfhS213+xb8ax4W160vNT8O+NfA2vqnlxeJfh7498NXukeNPAHiiCPMUHiPwdr2ia1HC0lut79nllif1WiunB43GZdiqONy/F4nA4zDz9ph8Xg69XDYmhOzjz0a9GUKtOXK3HmhJOza2bFKMZJxlFSi9HGSTT9U7pnzdoHxN/ay/ZiKW3iGHW/21fgZabUGpWaeHdC/a7+H+mIcb7uyH/CNfDr9ozRdLtULyzWbfDj4ui0gCRaf8ZvFV6TL93fBP8AaA+D37RPhe48XfB3x1pXjHTdN1B9F8R6fFHfaR4r8E+I4Y0lu/CfxC8Ea9a6X4x+H3jCwR0bUfCfjTQ9D8Q2AdGutNiWRGbyKvn74m/s4eCfiD4otPidoOqeKPg98ddH0+PTNA+PXwh1K28K/Euz063eSez0HxHNPYan4Y+KHgi3upHux8N/i34b8d/D2S8c358MjUUgvYerHYThnifmebYWnw7nM/hz/I8FShluJqPSLzzhvD+ww1OLtTjPMeHVga1GnGvisRk2f4+tdqE61H4G61P/AJ9VZPniv+ndZ3b6+5V5k20lUpQVj9QaK/Mjw/8AtefGX4A7NH/bE8FJ4v8Ah/afurb9rH4D+GNa1Hw9a2cY2x3nx4+BdnJ4g8c/C25VNn9peNfh9cfE/wCF58rUPEniaf4P6IINHt/0S8HeM/CHxD8MaJ428A+KfDvjbwb4m0+DVvDnizwlrWneIvDevaXcrut9R0fW9IubvTdSsp15iubO5mhfB2ucGvzvP+Ec64cjSxOLo0sVlWKqSp4HPctq/Xcmx0lH2ipUsZCMfq+MVHlr1sqzCngs4wdKpTePy/CymoHZSxFOtdRbU46ypTXLUj0u4veN9FOLlTk0+WcjpaKKK+YNgooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACvyf+DP8Ayc7/AMFNv+z0Phv/AOu3f+Cf1frBX5P/AAZ/5Od/4Kbf9nofDf8A9du/8E/q/T/Db/dPEX/shsN/68LgI4sZvhP+wl/+ouKPqCiivi79qqfXbfxV8LZdYtvjvd/BuPw/8T5vEtt+ztdfEvTvHNz8YIrv4cH4M2+s6n8Kb7S9c07wNLoh+Lh1i88W6ppnwmg15PCsnxKv7bSFt3rLMsb/AGfg6mL9n7X2c6EOVydOK9viKVD2lSooVHTo0fa+1rzVObhRhOShJqz93hbInxLnmEyZYn6o8TSx9b2saMcRVl9Qy7F5j9WwuGnXwsMTjsb9U+p4DDzxOHjXxtehSlWpqbmvtGivxX8QfFP4l/Ff4GeJPjfq/jn4keGfGXwk/wCCXn7PH7XXhCy+H3jvxR4D8Nat8aPiN4d+PfjLxZJ4s8L+F9S07Q/H2lz3Hwc8KaFB4Y8Y6fr/AIe0/Ste1pLLSYdQ1OG9g/Sbw78HvHOi/tE+PfjNf/GvxbrngTxb4SsfD+jfBK8TVR4V8JalbW3g+B9asGm8UXfh8PDL4Z1rUbB9I8FeH/Edxf8AxE8Yx+L/ABV4y0ex+HukeA/Iy7iKWayhLBZdWq4epPCz9s69CnOng8RPMsPPF1qNVwadHF5bUovD0Z16s6VajXh/y8p0/teJ/DKnwfSr08+4owGEzPDUs3oPAxy/MMVRxWe5ZQ4VzKlk2BxuEhXjJY7JeK8NjYZljqGX4Shi8Bjsur2awuKxP0FRRRX0p+VBRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAV8san+zhqHgTxPrnxQ/ZO8ez/s3/EzXryfWfFGhWGjDxP8As9fFfWpiHmvPi98CzqOi6Re6xqEgDan8RvhnrXww+L98yW0Wp/EDVdItm0S5+p6K9LLc3zDKpVvqdaKo4qmqONwWJoUMbluY0IyU44fMssxlKvgMwoRqKNWFHGYetTp1oQrQjGrThOMThGduZaxd4yTcZwfeE4tSi3s3Fq60ejseV+Cf2+tP8J67pPw6/bL8ER/sy+N9VvLfSPDnxJfW38U/stfEzU7q4Sz0+18H/GyfTtDj8F+JdXuJIorT4dfGrQ/h14pu9QlfTfBknxAtLb+3bn9E1ZXVWUhlYBlZSGVlIyGUjIIIOQRwRyK+Kte0DQvFWiar4a8UaLpPiTw5rthdaVrmga9ptnrGiazpd9C1ve6bqulahDcWOo2F5A7wXVneQTW9xC7RyxujFT8saD8JPjd+y4xv/wBjPxpp198O7cxyXH7IHxw13xDf/B1LZbrz7q1+B/xJhg8R+PP2c7yWF5YdO8P2umfEb4KaeiQ2Wj/CPwxJc3Gvwc+O4X4X4jTqZPUpcH53LbLcZXxGI4Tx9R2jGGCzPEzxOZcO1pvkiqWcVc0ympVqVsRiM8yHBUoUFcK9alpUTxFP+eKSrxXVyguWFVbu9NQmlaMaVWTbP19or4/+Bf7afwv+MfiUfC3xHpfif4E/tAwW97c3fwD+MsGlaB431Wz0tA2p+IfhrqmmarrHgv4zeCbUESzeL/hV4l8VadpUUsFv4pj8N6w82kW/2BX5lnOR5vw/jHl+c4CvgMV7OFenGtFOnicNUclRxmCxNOU8NjsDiFGUsLj8HWr4PFU17TD16tNqT7adWnVjzU5Kcb2dt4yW8ZJ2cZq/vRklKL0aTCiiivKLCiiigAooooAKKKKACiiigAooooAKKKKACvxu+FnxF+H2i/tSf8FNLbWfHXg7Sbl/2z/h+Ut9T8T6JYTsLT/gnX+wVpd0Viur6KRhbanp9/p1wQp8m+sby0k23FtNGn7I1/KZ4F/Zi/Z8+Pn7dH/BVnVfjL8IPAvxG1Tw/wDth+HdP0bUvE+h299f2Fhd/s4fBW5nsYbzCXBszcJ58dtJI8ME0lxLAkb3Nw0v23B+Ox+DwHH6y7D4TEYqvwTQjCGNxFbC0EoeIPAM5uVWhhsXUT5OblSoyTlZNxTbX1vCfD3D2eYmpV4nzPOcrynL6tGVatkOV4HNsxlLE4bH0qMaWEzDNcmw0o+2hTVSU8dBwpSnKMKk4xhL9sP+Fu/Cj/op/wAPP/C08N//ACyryP4paT+y78ZW0KXx9448LXV34bTWLbSNT8NfG3V/h9rMWl+I00+PxJ4eu9b+Hvjjwtq2q+E/Eq6TpI8SeEdVvb3wx4gOlaY2saTetp9mYfkH/h3J+wv/ANGufCL/AMJqP/47Xyp+3J+w3+yF8N/2Qv2iPHPgb9nf4XeG/Fvhv4XeJdQ0HXtP8NWov9Jvxa+THfWMkxlWC8gWV2trlU861m2XFu8VxFFKny+cZ3xLSyvMMRj8g4XxuDwuEr4zEYWpmuPrxrQwcHiuVUq2Q+ylNOipU+eyVRRleLSa/beCeA/CrG8X8NZbw54j+LuRZ5nGdZfkeW5thuDeHMBVwWIzzEU8o9q8XgPEZYyjQcMbOnivYc054adWnyVFJwl+wPi39mT4BfE+TwXrOs+Evtdl4W8N6N4d8OWvhPxn408I+EtU8D6Xe2Ot6B4U8ReG/AvibQfCnxB8C2N5ZWd/pPhXxnpfiPwvbnc9rpqx3VwJvoevPPhF/wAkn+GH/ZPPBX/qN6bXodfeYLD4WEPrVDCYbDVsbSw9TEzoUKdOdZxpJU1VnCEZVfZRk4U3UcuSLajZOx/OmfZnnOIrLJ8xzrNc0wWQ4rMcLldDMMdisVQwMKuKbxTwWHr1qtLB/XKlGFbExw8YKtUjGdTnlFNFFFFdx4AUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQB5z8T/AIR/Db4zeHF8K/E/wdo/i/Rre/ttY0xdRili1Pw9r9gWbTPE/hPX7GW01/wh4s0eRjcaJ4r8L6npHiPRLrbd6Vqlncoso8s8PeKv2s/2XRHBpV3rn7afwMsgijwr4q1rQ9I/a18C6bHncnhb4h65c6F4D/aDsbRCsdrovxRvvh58Ro7K3nvNQ+LfxI12a20uf6Zor2MLnNWlg3lWYYXB55kcqkqsslzenVrYSnWny8+IwFahWw+YZPjKjhT9rjMmxuAxOJhThh8XUxGEc8POHBc3PCUqVTb2lOyk0tlNNOFSK1tGpGSje8UpWa9L+Bf7SnwY/aP0bVdV+E/jGHWNQ8M3kOleOfBOsafqnhP4l/DbXpoBcL4c+Jfw28U2ekeNvAWvGE+dDp3ifQ9NkvrQx6hppvdNnt7yb3WvzJ+K37O3w8+K+s6P43n/ALf8A/F7wrZy2Xgj46fC3WZfBHxg8HWss32l9L0/xdYRSjXfCdzeCO71f4c+N7DxX8M/E00US+KvBuuQIIar6B+1F+0J+zuU0v8Aal8Iz/G/4V2uI4f2nPgP4Ovn8YeH7FCcXnx2/Zy0T+19ajjs7WMSav8AEX4Cv4v0nUbyS51G9+Dnwr8OWrTR+FjuAsFmt6/BWMrVsQ9ZcKZ1Ww8M7T2UMmzKFPCZdxI5PljTwkKGU55Wr1oYXAZLmSpVMY9YYqUNMRFJf8/6afs/+4kG5To/4m6lNJc0qkLqJ+n1FcV8O/iR4A+Lng3QviH8LvGnhj4heBfE1oL7QPF3g/WtP8QeH9Wtt7RO9nqmmT3FrK8E8cltdQ+YJ7S6imtbqOG4hliTta/MsRh8RhK9bC4uhWw2Kw1WpQxGGxFKdGvQr0pOFWjWo1IxqUqtOcZQqU5xjOEk4ySaaO1NSSlFpppNNO6aeqaa0aa1TW4UUV4d+0X8ddK/Zx+Fl18UNW8FeOfiN/xX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0.0000000 0.0000000 0 4.06.1.1.51Q Càlcul tercer angle d'un triangle qualsevol En un triangle qualsevol, l'angle A val #a º, i l'angle B val #b º. Quants graus mesura l'angle C?

Format de la resposta: 35 (sense el símbol de graus)

]]> N'hi ha prou amb restar els dos angles de 180º, ja que la suma dels tres angles d'un triangle és 180º:
C = 180º - #aº - #bº

]]> 1.0000000 0.5000000 0 0 #s_31 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>45</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>44</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_31</mi><mo>=</mo><mo>(</mo><mn>180</mn><mo>-</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo></math></input></command></group></library></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#s_31</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> 4.06.1.1.52Q TercerAngleTriangleIsòceles En un triangle isòsceles, l'angle desigual A val #a º. Quants graus mesuren els angles iguals?

Format de la resposta: 35º30'

]]>

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>65</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>A</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mrow><mn>2</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>53</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>63.5</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que els dos angles són iguals, cada un d'ells mesura la meitat de 180º - Aº:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mn mathvariant=¨bold¨»180«/mn»«mo mathvariant=¨bold¨»§#186;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»A«/mi»«mo mathvariant=¨bold¨»§#186;«/mo»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.06.1.1.61Q TercerAngleTriangleRectangle En un triangle rectangle, un dels angles fa #a º. L'altre angle agut fa doncs:

{#1} º

]]> 1.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>89</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Com que els dos angles aguts han de sumar 90º,
l'angle desconegut mesura : 90º - #a

]]> 4.06.1.1.62Q Trobar2AnglesTriangleRectangle En un triangle rectangle, un dels angles fa #a º. Els dos altres angles fan doncs:

El més gran: {#1} º
El més petit: {#2} º

]]> 2.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>84</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Com que és rectangle, l'angle més gran mesura 90º.
I com que els dos angles aguts han de sumar 90º, l'angle desconegut més petit mesura: 90º - #a = #b]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.1 Angles i triangles/4.06.1.2 Construcció de triangles rectangles 4.06.1.2.10 TEORIA DIBUIXTRIANGLESRECTANGLES

Dibuixar un triangle rectangle

Si ens donen b i C(90º-B): es mesura el costat vertical b, i des del punt C, es mesura l'angle C.

Si ens donen c i B(90º-C): es mesura el costat horitzontal c, i dels del punt B, es mesura l'angle B.

Si ens donen a i B(90º-C): marquem el punt B en una recta. Mesurem l'angle B i tracem la recta BC. Mesurem a i des de C, tracem la perpendicular.

]]> 0.0000000 0.0000000 0 4.06.1.2.11Q DibuixTriangleConegutsBb Dibuixa un triangle rectangle on «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math» cm

Mesura la hipotenusa a (en centímetres, als dècims)

En l'eix vertical mesures b i marques el vèrtex C.

Dedueixes l'angle C (90º - B)

En el punt C, mesures l'angle C amb el transportador.

Traces el costat a i el mesures.

]]> 4.06.1.2.12Q DibuixTriangleConegutsCc Dibuixa un triangle rectangle on «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math» cm

Mesura la hipotenusa a (en centímetres, als dècims)

En l'eix horitzontal mesures c i marques el vèrtex B.

Dedueixes l'angle B = (90º - B)

En el punt B, mesures l'angle B amb el transportador.

Traces el costat a i el mesures.

]]> 4.06.1.2.13Q DibuixTriangleConegutsBa Dibuixa un triangle rectangle on «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#186;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math» cm

Mesura el costat b (en centímetres, als dècims)

En el punt B, mesura l'angle B amb el transportador.

Traça el costat a i mesura'l.

Dibuixa la perpendicular des de l'extrem del costat A.

Mesura la perpendicular (b)

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.1 Angles i triangles/4.06.1.3 Teorema de Pitàgores 4.06.1.3.10 TEORIA: TEOREMA DE PITÀGORES Teorema de Pitàgores

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»a«/mi»«mo»=«/mo»«msqrt»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«/msqrt»«mo»§#8660;«/mo»«mi»b«/mi»«mo»=«/mo»«msqrt»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«mi»c«/mi»«mn»2«/mn»«/msup»«/msqrt»«mo»§#8660;«/mo»«mi»c«/mi»«mo»=«/mo»«msqrt»«msup»«mi»a«/mi»«mn»2«/mn»«/msup»«mo»-«/mo»«msup»«mi»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«/math»

]]> 0.0000000 0.0000000 0 4.06.1.3.11Q Pitàgores: a En un triangle rectangle, calculeu la hipotenusa a si els catets mesuren: b = #b i c = #c.

Format de la resposta:arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r_61 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi><mo>=</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>44</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2161</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_61</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Aplica directament el teorema de Pitàgores
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfenced»«/msqrt»«/mrow»«/mstyle»«/math»

POSA PARÈNTESIS A LA CALCULADORA

]]> 4.06.1.3.12Q Pitàgores: b En un triangle rectangle, calculeu el costat b si el catet c mesura #b i la hipotenusa a = #a.

Format de la resposta:arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r_61 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>&gt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>,</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>357</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_61</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Apliquem el teorema de Pitàgores:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/mrow»«/mfenced»«/msqrt»«/mrow»«/mstyle»«/math»

POSA PARÈNTESIS A LA CALCULADORA

]]> 4.06.1.3.13Q Pitàgores: c En un triangle rectangle, calculeu el costat c si el catet b mesura #b i la hipotenusa a = #a.

Format de la resposta:arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r_61 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a</mi><mo>&gt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn><mo>,</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_61</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>357</mn></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_61</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Aplica el teorema de Pitàgores:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«msup»«mo mathvariant=¨bold¨»§#160;«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»)«/mo»«/msqrt»«/mrow»«/mstyle»«/math»

POSA PARÈNTESIS A LA CALCULADORA!!!

]]> 4.06.1.3.21Q Pitàgores: Figura Amb la figura següent,

calcula el costat c, si b = #b_1 i a = #a_1

Resultat arrodonit a la unitat

]]> 1.0000000 0.5000000 0 0 #r <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo> </mo><mi>Dibuixar</mi><mo> </mo><mi>triangle</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>y_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>y_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>,</mo><mi>y_1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>v_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_2</mi><mo>,</mo><mi>y_2</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><apply><scalarproduct/><mi>v_1</mi><mi>v_2</mi></apply><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>y_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>x_2</mi><mo>,</mo><mi>y_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>y_1</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x_2</mi><mo>,</mo><mi>y_2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>mostrar_malla</mi><mo>=</mo><mi>fals</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>T</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>C</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>negre</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mo> </mo><mi>Definir</mi><mo> </mo><mi>lados</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>segment</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>longitud</mi><mo>(</mo><mi>segment</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>H</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>a</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi><mo>,</mo><mi>etiqueta</mi><mo>=</mo><mi>a_1</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>segment</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>longitud</mi><mo>(</mo><mi>segment</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>b</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi><mo>,</mo><mi>etiqueta</mi><mo>=</mo><mi>b_1</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>segment</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>longitud</mi><mo>(</mo><mi>segment</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>J</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S</mi><mo>,</mo><mi>c</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>fals</mi><mo>,</mo><mi>etiqueta</mi><mo>=</mo><mi>c_1</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><msqrt><mrow><msup><mi>a_1</mi><mn>2</mn></msup><mo>-</mo><msup><mi>b_1</mi><mn>2</mn></msup></mrow></msqrt></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mn>6</mn><mo>,</mo><mo>-</mo><mn>6</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mn>0</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>6</mn><mo>,</mo><mo>-</mo><mn>6</mn></mrow></mfenced><mo>-</mo><mfenced><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Només cal aplicar el teorema de Pitàgores.

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.2 Semblança/4.06.2.1 Triangles semblants 4.06.2.1.10 TEORIA SEMBLANÇA Semblança Definició
Dues figures són semblants si tenen la mateixa forma.

Angles de figures semblants tsemblants

Si dues figures són semblants, tenen els angles homòlegs iguals

Costats de figures semblants

tsemblantscostats

Els costats homòlegs de figures semblants són proporcionals:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»8«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»6«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»10«/mn»«mn mathvariant=¨bold¨»5«/mn»«/mfrac»«/mrow»«/mstyle»«/math»

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0.0000000 0.0000000 0 4.06.2.1.20 TEORIA TRIANGLES SEMBLANTS Triangles semblants

Definició

Dos triangles són semblants si tenen els 3 angles iguals. Com que la suma dels 3 angles és sempre 180º, n'hi ha prou amb què tinguin 2 angles iguals.

Criteris de semblança

Dos triangles són semblants si tenen un angle igual, i els costats que el delimiten proporcionals.

I també dos triangles són semblants si tenen els 3 costats proporcionals.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»a«/mi»«mrow»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mrow»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

B = {#2}º

C = {#3}º

]]> 3.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>85</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command></group></library></session></wirisCasSession></question> Com que són semblants, els angles són iguals.

]]> 4.06.2.1.22Q Semblança angles T. rectangles En un triangle rectangle, un angle mesura #a º.
En un altre triangle rectangle, un angle mesura #b º.

N'hi ha prou per afirmar que són semblants?

]]> 1.0000000 1.0000000 0 Vertader Molt bé!

]]> Fals Si perquè en el primer triangle el tercer angle mesura #b º (restant de 90º), i en el segon triangle, el tercer angle mesura #a º (restant de 90º).
I, per tant, com que són rectangles, tenen els 3 angles iguals: 90º #a º i #b º.

]]> <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>67</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.2.1.31Q CàlculRaóSemblança Dos triangles són semblants:
En el triangle més petit, els costats són {#a_1, #a_2, a}
En el triangle més gran, els costats homòlegs són {#b_1, b, #b_3}.

Quina és la raó de semblança (en fracció) per passar del triangle petit al gran? {#1}
Quina és la raó de semblança (en fracció) per passar del triangle gran al petit? {#2}
Quin és l'homòleg b del 2n costat del triangle petit en el triangle gran? {#3}
Quin és l'homòleg a del 3r costat del triangle gran en el triangle petit? {#4}

]]> 4.0000000 0.5000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mn>40</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mn>40</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mn>40</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>a_1</mi><mo>+</mo><mi>a_2</mi><mo>&gt;</mo><mi>a_3</mi></mrow></apply><mrow><mi>a_1</mi><mo>+</mo><mi>a_3</mi><mo>&gt;</mo><mi>a_2</mi></mrow></apply><mrow><mi>a_2</mi><mo>+</mo><mi>a_3</mi><mo>&gt;</mo><mi>a_1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mfrac><mn>7</mn><mn>5</mn></mfrac><mo>,</mo><mfrac><mn>11</mn><mn>8</mn></mfrac></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi><mo>=</mo><mfrac><mn>1</mn><mi>f_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>f_1</mi><mo>*</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>f_1</mi><mo>*</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>f_1</mi><mo>*</mo><mi>a_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>a_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1880</mn><mo>,</mo><mn>1480</mn><mo>,</mo><mn>760</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>,</mo><mi>b_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2632</mn><mo>,</mo><mn>2072</mn><mo>,</mo><mn>1064</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> Els costats homòlegs (que mantenen la proporció) són #a_1 i #b_1, #a_2 i b, i a i #b_3.

#a_1 i #b_1 en permeten calcular la proporció:

Per passar de petit a gran, la raó serà #b_1/#a_1 = #f_1
Per passar de gran a petit, la raó és #a_1/#b_1 = #f_2

Per calcular b, cal passar #a_2 de petit a gran amb la raó corresponent.

Per calcular a, cal passar #b_3 de gran a petit amb la raó corresponent.

]]> 4.06.2.1.41Q Semblança i Pitàgoes Considera dos triangles semblants com els de la figura:

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math», quina és la longitud de a' ?

Format: arrodonida als centèsims

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>51</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>r</mi><mo>*</mo><msqrt><mrow><msup><mi>b1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c1</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a2</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>c1</mi><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><msqrt><mrow><msup><mi>b2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c2</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>26</mn><mo>,</mo><mn>104</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>,</mo><mi>c2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>74</mn><mo>,</mo><mn>296</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>,</mo><mi>a11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>*</mo><msqrt><mn>1538</mn></msqrt><mo>,</mo><mn>8</mn><mo>*</mo><msqrt><mn>1538</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>313.74</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer, calcules la longitud de la hipotenusa en el triangle petit amb el teorema de Pitàgores: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«msup»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«msup»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»

Desprès, determines la raó de semblança entre els dos triangles: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Finalment, multipliques la hipotenusa en el triangle petit per la raó.

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.2 Semblança/4.06.2.2 Teorema de Tales 4.06.2.2.10 TEORIA: TEOREMA DE TALES Teorema de Tales Si 2 segments (amb mateix origen) tallen 2 rectes paral·leles, els segments que determinen són proporcionals.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»D«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»E«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»A«/mi»«mi mathvariant=¨bold¨»C«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»D«/mi»«mi mathvariant=¨bold¨»E«/mi»«/mrow»«mi mathvariant=¨bold¨»BC«/mi»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.06.2.2.11 Exercici/teorema de Thales

Calcula la longitud dels costats indicats si:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»AD«/mi»«mi mathvariant=¨bold¨»AE«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

i AE = 10 cm i AC = 13 cm

Format: als dècims
AD = {#1} AB = {#2}

]]> 2.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo></mrow><mn>10</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R_1</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R_2</mi><mo>=</mo><mn>13</mn><mo>*</mo><mi>r</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>17</mn><mn>10</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22.1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Per calcular AD, només cal substituir AE per 10 en l'expressió que et donen:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»AD«/mi»«mi mathvariant=¨bold¨»AE«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«/mstyle»«/math» i aïllar AD.

Per calcular AB, fixa't en què AB és proporcional a AD

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.2 Semblança/4.06.2.3 Problemes de semblança 4.06.2.3.10 TEORIA: ESCALES Escales

Per indicar la raó de semblança

entre la distància real i la distància en el plànol ,

s'escriu així: Escala = 1:R

on R és el quocient Distància real/Distància en el plànol.

Exemple: Si 60 m reals són 3cm en el pla, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathvariant=¨italic¨ mathsize=¨12px¨»«mfrac»«mrow»«mn»6«/mn»«mo».«/mo»«mn»000«/mn»«mi»c«/mi»«mi»m«/mi»«/mrow»«mrow»«mn»3«/mn»«mi»c«/mi»«mi»m«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mn»2000«/mn»«/mstyle»«/math»

i l'escala és 1/2.000

]]> 0.0000000 0.0000000 0 4.06.2.3.11Q Dibuix a escala En un triangle rectangle, un dels angles aguts fa #k º, i la hipotenusa #h metres.
Feu un dibuix a escala per deduir quant fan els dos catets:

Catet més petit: {#1} m
Catet més gran: {#2} m

Poseu el resultat en forma de nombre natural.

]]> 2.0000000 0.1000000 0 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>85</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mrow><mi>k</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo> </mo><mi>arrodonir</mi><mo>(</mo><mi>h</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>h</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfenced><msqrt><mrow><msup><mi>c_1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c_2</mi><mn>2</mn></msup></mrow></msqrt></mfenced><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c_1</mi><mo>&lt;</mo><mi>c_2</mi></mrow><mrow><mi>w_1</mi><mo>=</mo><mi>c_1</mi></mrow><mrow><mi>w_1</mi><mo>=</mo><mi>c_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>c_1</mi><mo>&gt;</mo><mi>c_2</mi></mrow><mrow><mi>w_2</mi><mo>=</mo><mi>c_1</mi></mrow><mrow><mi>w_2</mi><mo>=</mo><mi>c_2</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>k</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>h</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>,</mo><mfrac><mrow><mn>23</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac><mo>,</mo><mn>74</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>73.926</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>29</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> No és gens útil fer trampa!

]]> 4.06.2.3.12Q Escala d'un mapa

En un mapa, s'ha representat una distància de #k metres per #c centímetres.

L'escala del mapa és

1 : {#1}

En el mapa, dos pobles distants de #m metres queden separats per {#2} cm

]]> ]]> 2.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>19</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>c</mi><mo>≠</mo><mi>r_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>500</mn><mo>,</mo><mn>1000</mn><mo>,</mo><mn>2000</mn><mo>,</mo><mn>5000</mn><mo>,</mo><mn>25000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfrac><mrow><mi>c</mi><mo>*</mo><mi>r_1</mi></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k_1</mi><mo>=</mo><mn>100</mn><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mi>r_2</mi><mo>*</mo><mi>r_1</mi></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>,</mo><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>80.</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Per trobar l'escala, cal transformar els #k metres a centímetres i després dividir aquest resultat #k_1 per #c. Es tracta de reduir a la unitat.
Per trobar la distància, n'hi ha prou amb aplicar la proporcionalitat (regla de 3)
]]> 4.06.2.3.20 TEORIA: DISTÀNCIES INACCESSIBLES Distàncies inaccessibles

Si es coneixen les distàncies en un dels triangles,

es poden deduir en l'altre.

Sovint cal emprar el teorema de Pitàgores

]]> 0.0000000 0.0000000 0 4.06.2.3.21Q Altura edifici amb ombra

L'ombre de la torre és de #o1 m. A la mateixa hora, un pal de #m2 m projecta una ombra de #o2 m.

Quina alçada té la torre?

Format: metres als dècims

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»o«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 4.06.2.3.51Q Problema superfície semblant Per pintar les parets d'una habitació rectangular de #l m de llarg, #a m d'ample i #h m d'alt, s'han utilitzat #k kilos de pintura.

Quants kilos de pintura calen per pintar les parets d'una habitació semblant si fa #l2 m de llarg?

Format: arrodonit als centèsims

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>l</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>650</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>450</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>h</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>201</mn><mo>,</mo><mn>260</mn></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>l</mi><mo>></mo><mi>a</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>nr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>dr</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mfrac><mi>nr</mi><mi>dr</mi></mfrac></mtd></mtr></mtable><mrow><mi>r</mi><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>l</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>l</mi><mo>*</mo><mi>h</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>h</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>l</mi><mo>*</mo><mi>h</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>h</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>arrodoneix</mi><mfenced><mfrac><mi>S1</mi><mi>k1</mi></mfrac></mfenced><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>k</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>h</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.98</mn><mo>,</mo><mn>2.66</mn><mo>,</mo><mn>2.34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>,</mo><mi>S2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>35.755</mn><mo>,</mo><mn>48.667</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16.33</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">6</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula la raó de semblança:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»l«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»l«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Com que la raó entre les longituds és r, la raó entre les superfícies pintades és r².

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.3 Raons trigonomètriques/4.06.3.1 Definició de les raons 4.06.3.1.10 TEORIA: RAONS TRIGONOMÈTRIQUES

Raons trigonomètriques

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»oposat«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«mi mathvariant=¨bold¨»hipotenusa«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cosB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»adjacent«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«mi mathvariant=¨bold¨»hipotenus«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tgB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»oposat«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«mrow»«mi mathvariant=¨bold¨»adjacent«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sinB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»cosB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tgB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfrac mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»c«/mi»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.06.3.1.11Q Trobar les raons amb els 3 costats En un triangle rectangle, els costats mesuren a = #a, b = #b, c = #c. Determineu el sinus, el cosinus i la tangent de l'angle B.

Format de la resposta: fraccions simplificades.

]]> 1.0000000 0.5000000 0 0 sin B =#scos B =#c_stg B =#t]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><msqrt><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mi>b</mi><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_s</mi><mo>=</mo><mfrac><mi>c</mi><mi>a</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>b</mi><mi>c</mi></mfrac></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo> </mo><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mspace linebreak="newline"/><mi>cos</mi><mo> </mo><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mi>s</mi><mspace linebreak="newline"/><mi>tg</mi><mo> </mo><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Has simplificat les fraccions?

El costat oposat a l'angle B és #b.

El costat adjacent a l'angle B és #c

La hipotenusa és #a.

Per fer les fraccions, fes servir la definició de sinus, cosinus i tangent.

]]> 4.06.3.1.12Q Trobar les raons amb els 3 costats_2 En un triangle rectangle, els costats mesuren a = #a, b = #b, c = #c. Determineu el sinus, el cosinus i la tangent de l'angle B.

Format de la resposta: fraccions simplificades.

El costat oposat a l'angle B és #b.

El costat adjacent a l'angle B és #c

La hipotenusa és #a.

Per fer les fraccions, fes servir la definició de sinus, cosinus i tangent.

]]> 4.06.3.1.21Q Trobar les raons amb 2 costats En un triangle rectangle,

els costats mesuren b = #b, c = #c. (arrodoniu a a les unitats)

Determineu el sinus, el cosinus i la tangent de l'angle B.

Format de la resposta: fraccions simplificades.

El costat oposat a l'angle B és #b.

El costat adjacent a l'angle B és #c

La hipotenusa és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«msqrt mathcolor=¨#007F00¨»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math».

Per fer les fraccions, fes servir la definició de sinus, cosinus i tangent.

]]> 4.06.3.1.22Q Trobar les raons amb 2 costats_2 En un triangle rectangle,

els costats mesuren b = #b, c = #c. (arrodoniu a a les unitats)

Determineu el sinus, el cosinus i la tangent de l'angle B.

Format de la resposta: fraccions simplificades.

El costat oposat a l'angle B és #b.

El costat adjacent a l'angle B és #c

Per fer les fraccions, fes servir la definició de sinus, cosinus i tangent.

]]> 4.06.3.1.51Q RaonsTrigonomètriques+Semblança Considera els dos triangles on l'angle B és el que delimiten a i c.

Si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mrow»«/mstyle»«/math»,

a) Quina fracció simplificada correspon a sinB en el triangle petit?

b) Quina fracció simplificada correspon a sinB en el triangle gran?

c) Es sinus depen només de l'angle (respon 1) o de la mida del triangle (respon 2)

]]> 1.0000000 0.5000000 0 0 a)=#sol1b)=#sol2c)=#sol3]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>21</mn><mo>,</mo><mn>29</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>19</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>b1</mi></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>b1</mi><mi>a1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>b2</mi><mi>a2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn><mo>,</mo><mn>115</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn><mo>,</mo><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14</mn><mn>23</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14</mn><mn>23</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> En el triangle petit, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sinB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

En el triangle gran, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sinB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

És fàcil comparar les fraccions simplificades per respondre!

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.3 Raons trigonomètriques/4.06.3.2 Relacions trigonomètriques 4.06.3.2.10 TEORIA: RELACIONS FONAMENTALS

Relacions fonamentals

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msup mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«/math»

és el mateix que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»sin§#945;«/mi»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»+«/mo»«msup mathcolor=¨#00007F¨»«mfenced mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»cos§#945;«/mi»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math»

Se'n dedueix: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»sin§#945;«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»cos«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»cos§#945;«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»§#177;«/mo»«msqrt»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»sin«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mi mathvariant=¨bold¨»§#945;«/mi»«/msqrt»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tg§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»sin§#945;«/mi»«mi mathvariant=¨bold¨»cos§#945;«/mi»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 4.06.3.2.11Q Cosinus a partir del sinus El sinus d'un angle a és de #s. Calculeu el seu cosinus.

Format de la resposta: 0.32 (arrodonit als centèsims; i punt i no coma!)

]]> 1.0000000 0.5000000 0 0 #c <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>92</mn><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>s</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>c1</mi></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.49</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.87</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#c</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msqrt mathcolor=¨#007F00¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»

]]> 4.06.3.2.12Q Sinus a partir del cosinus El cosinus d'un angle a és de #c. Calculeu el seu sinus.

Format de la resposta: 0.32 (arrodonit als centèsims; i punt i no coma!)

]]> 1.0000000 0.5000000 0 0 #s <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>92</mn><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>s</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>c1</mi></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.93</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.37</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#s</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">6</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msqrt mathcolor=¨#007F00¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»

]]> 4.06.3.2.13Q Tangent a partir del sinus El sinus d'un angle a és de #s. Calculeu la seva tangent.

Format de la resposta: 0.32 (arrodonit als centèsims; i punt i no coma!)

]]> 1.0000000 0.5000000 0 0 #t <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>92</mn><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>-</mo><msup><mi>s</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mfrac><mi>s</mi><mi>c1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>t1</mi></mrow></mfenced></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.7766</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.63</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.81</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#t</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer es calcula el cosinus: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«msqrt mathcolor=¨#007F00¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»s«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/math»

Després es divideix el sinus pel cosinus per trobar la tangent, i s'arrodoneix.

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.4 Càlcul de raons trigomètriques 4.06.4.10 TEORIA: CALCULADORA

Raons trigonomètriques: calculadora

Per calcular el sinus, el cosinus o la tangent d'un angle de 28º, s'escriu, en el cas del sinus: sin 28 =.

Per calcular l'angle que té per sinus 0,25 es tecleja: shift sin 0.25 =.

ATENCIÓ: CONTROLEU SEMPRE SI TENIU LA CALCULADORA

EN GRAUS (D) O EN RADIANTS (R)

]]> 0.0000000 0.0000000 0 4.06.4.11 Calcular sin, cos i tg amb calculadora Completeu la taula següent:

angle	sinus	cosinus	tangent
#a_1º	{#1}	{#2}	{#3}
#a_2º	{#4}	{#5}	{#6}
#a_3º	{#7}	{#8}	{#9}
#a_4º	{#10}	{#11}	{#12}

Format: als deu mil·lèsims

]]> 12.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>a_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_2</mi><mo>=</mo><mfrac><mrow><mi>a_2</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_3</mi><mo>=</mo><mfrac><mrow><mi>a_3</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_4</mi><mo>=</mo><mfrac><mrow><mi>a_4</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr></mtable><mrow><mi>cos</mi><mo>(</mo><mi>r_1</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_2</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_3</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_4</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_1</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r_1</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_1</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_1</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r_1</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_2</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r_2</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_2</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_2</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r_2</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_3</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r_3</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_3</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_3</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r_3</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s_4</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r_4</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_4</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t_4</mi><mo>=</mo><mfrac><mrow><mi>arrodonir</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r_4</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>r_1</mi><mo>,</mo><mi>s_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>t_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97</mn><mo>,</mo><mfrac><mrow><mn>97</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac><mo>,</mo><mn>0.9925</mn><mo>,</mo><mo>-</mo><mn>0.1219</mn><mo>,</mo><mo>-</mo><mn>8.1443</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_2</mi><mo>,</mo><mi>r_2</mi><mo>,</mo><mi>s_2</mi><mo>,</mo><mi>c_2</mi><mo>,</mo><mi>t_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo>,</mo><mfrac><mrow><mn>31</mn><mo>*</mo><pi/></mrow><mn>30</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.1045</mn><mo>,</mo><mo>-</mo><mn>0.9945</mn><mo>,</mo><mn>0.1051</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_3</mi><mo>,</mo><mi>r_3</mi><mo>,</mo><mi>s_3</mi><mo>,</mo><mi>c_3</mi><mo>,</mo><mi>t_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>197</mn><mo>,</mo><mfrac><mrow><mn>197</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.2924</mn><mo>,</mo><mo>-</mo><mn>0.9563</mn><mo>,</mo><mn>0.3057</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_4</mi><mo>,</mo><mi>r_4</mi><mo>,</mo><mi>s_4</mi><mo>,</mo><mi>c_4</mi><mo>,</mo><mi>t_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>246</mn><mo>,</mo><mfrac><mrow><mn>41</mn><mo>*</mo><pi/></mrow><mn>30</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.9135</mn><mo>,</mo><mo>-</mo><mn>0.4067</mn><mo>,</mo><mn>2.246</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">6</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4.06.4.12Q 2 angles Calcular sin, cos i tg 2AnglesCalculadora Completa la taula següent emprant la calculadora:

angle	sinus	cosinus	tangent
#a_1º	{#1}	{#2}	{#3}
#a_2º	{#4}	{#5}	{#6}

Arrodoneix als deu mil·lèsims

]]> 6.0000000 0.5000000 0 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_1</mi><mo>=</mo><mfrac><mrow><mi>a_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_2</mi><mo>=</mo><mfrac><mrow><mi>a_2</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_3</mi><mo>=</mo><mfrac><mrow><mi>a_3</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr><mtr><mtd><mi>a_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>360</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>r_4</mi><mo>=</mo><mfrac><mrow><mi>a_4</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></mtd></mtr></mtable><mrow><mi>cos</mi><mo>(</mo><mi>r_1</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_2</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_3</mi><mo>)</mo><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r_4</mi><mo>)</mo><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>r_1</mi><mo>,</mo><mi>s_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>t_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>97</mn><mo>,</mo><mfrac><mrow><mn>97</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac><mo>,</mo><mn>0.9925</mn><mo>,</mo><mo>-</mo><mn>0.1219</mn><mo>,</mo><mo>-</mo><mn>8.1443</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_2</mi><mo>,</mo><mi>r_2</mi><mo>,</mo><mi>s_2</mi><mo>,</mo><mi>c_2</mi><mo>,</mo><mi>t_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>186</mn><mo>,</mo><mfrac><mrow><mn>31</mn><mo>*</mo><pi/></mrow><mn>30</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.1045</mn><mo>,</mo><mo>-</mo><mn>0.9945</mn><mo>,</mo><mn>0.1051</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_3</mi><mo>,</mo><mi>r_3</mi><mo>,</mo><mi>s_3</mi><mo>,</mo><mi>c_3</mi><mo>,</mo><mi>t_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>197</mn><mo>,</mo><mfrac><mrow><mn>197</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.2924</mn><mo>,</mo><mo>-</mo><mn>0.9563</mn><mo>,</mo><mn>0.3057</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_4</mi><mo>,</mo><mi>r_4</mi><mo>,</mo><mi>s_4</mi><mo>,</mo><mi>c_4</mi><mo>,</mo><mi>t_4</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>246</mn><mo>,</mo><mfrac><mrow><mn>41</mn><mo>*</mo><pi/></mrow><mn>30</mn></mfrac><mo>,</mo><mo>-</mo><mn>0.9135</mn><mo>,</mo><mo>-</mo><mn>0.4067</mn><mo>,</mo><mn>2.246</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">6</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4.06.4.50 TEORIA: RAONS 0,30,45,60,90 Raons de Raons de 0º,30º,45º, 60º, 90º sin cos tg 0º 0 1 0 30º 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/mstyle»«/math» 45º «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» 1 60º «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» 1/2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mstyle»«/math» 90º 1 0 +∞ ]]> 0.0000000 0.0000000 0 4.06.4.51 sin 0,30,45,60,90 Sense emprar la calculadora, quin és el sinus de l'angle de #a º?

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 #w_4 #w_5 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>45</mn><mo>,</mo><mn>60</mn><mo>,</mo><mn>90</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>30</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>45</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>60</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_2</mi></mtd></mtr></mtable></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_5</mi></math></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.52 cos 0,30,45,60,90 Sense emprar la calculadora, quin és el cosinus de l'angle de #a º?

]]> Mireu la taula!

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 #w_4 #w_5 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>45</mn><mo>,</mo><mn>60</mn><mo>,</mo><mn>90</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>30</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>45</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>60</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_2</mi></mtd></mtr></mtable></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.53 tg 0,30,45,60,90 Sense emprar la calculadora, quina és la tangent de l'angle de #a º?

]]> Mireu la taula!

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 #w_4 #w_5 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>0</mn><mo>,</mo><mn>30</mn><mo>,</mo><mn>45</mn><mo>,</mo><mn>60</mn><mo>,</mo><mn>90</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><msqrt><mn>3</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_5</mi><mo>=</mo><cn>+∞</cn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>30</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>45</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>60</mn></mrow><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_2</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_5</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>w_1</mi><mo>=</mo><mi>r_5</mi></mtd></mtr><mtr><mtd><mi>w_2</mi><mo>=</mo><mi>r_1</mi></mtd></mtr><mtr><mtd><mi>w_3</mi><mo>=</mo><mi>r_3</mi></mtd></mtr><mtr><mtd><mi>w_4</mi><mo>=</mo><mi>r_4</mi></mtd></mtr><mtr><mtd><mi>w_5</mi><mo>=</mo><mi>r_2</mi></mtd></mtr></mtable></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.61 Escriure sin30º Sense emprar la calculadora, escriu el sinus de l'angle de 30º.

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.62 Escriu sin45º Sense emprar la calculadora escriu el sinus de l'angle de 45º.

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 4.06.4.63 Escriu sin 90º Sense emprar la calculadora, quin és el sinus de l'angle de 90º.

]]> Mira la taula en els apunts.

]]> 1.0000000 0.5000000 0 true true abc #w_4 #w_1 #w_2 #w_3 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi><mo>=</mo><mn>1</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.64 Escriu tg 60º La tangent de l'angle de 60º és igual a:

]]>

]]> 1.0000000 0.5000000 0 true true abc #w_1 #w_2 #w_3 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><msqrt><mn>3</mn></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>3</mn></msqrt><mn>3</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.71 Angle que té per raó (arrel 3)/2 La raó trigonomètrica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» correspon a:

]]>

]]> 1.0000000 0.5000000 0 false true abc #w_1 #w_2 #w_3 #w_4 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>&quot;</mo><mi>sin</mi><mo> </mo><mn>60</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>&quot;</mo><mi>cos</mi><mo> </mo><mn>30</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mo>&quot;</mo><mi>sin</mi><mo> </mo><mn>30</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi><mo>=</mo><mo>&quot;</mo><mi>cos</mi><mo> </mo><mn>60</mn><mo>º</mo><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sin</ms><mo> </mo><ms>60º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cos</ms><mo> </mo><ms>30º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sin</ms><mo> </mo><ms>30º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cos</ms><mo> </mo><ms>60º</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4.06.4.72 Angle que té per raó 1/2 La raó trigonomètrica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math» correspon a:

]]>

]]> 1.0000000 0.5000000 0 false true abc #w_1 #w_2 #w_3 #w_4 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mo>&quot;</mo><mi>sin</mi><mo> </mo><mn>30</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi><mo>=</mo><mo>&quot;</mo><mi>cos</mi><mo> </mo><mn>60</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi><mo>=</mo><mo>&quot;</mo><mi>sin</mi><mo> </mo><mn>60</mn><mo>º</mo><mo>&quot;</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi><mo>=</mo><mo>&quot;</mo><mi>cos</mi><mo> </mo><mn>30</mn><mo>º</mo><mo>&quot;</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sin</ms><mo> </mo><ms>30º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cos</ms><mo> </mo><ms>60º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>sin</ms><mo> </mo><ms>60º</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cos</ms><mo> </mo><ms>30º</ms></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession></question> 4t ESO/4.06 TRIGONOMETRIA/4.06.5 Resolució de triangles rectangles/4.06.5.1 Resolució segons els costats i//o l'angle coneguts 4.06.5.1.10 TEORIA: Resolució amb b i c (Pitàgores)

Resolució coneguts 2 costats:Pitàgores

1. Coneguts b i c, s'aplica el teorema de Pitàgores per trobar la hipotenusa a: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msqrt mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mstyle»«/math».

2. Si es coneix a i b (o a i c) es calcula el costat que falta amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msqrt mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»o«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«msqrt mathcolor=¨#00007F¨»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»-«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»

3. Per determinar els angles aguts, es fan servir les raons trigonomètriques: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»s«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»n«/mi»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathsize=¨12px¨»b«/mi»«mi mathvariant=¨bold¨ mathsize=¨12px¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»§#8201;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»=«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»s«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨ mathsize=¨12px¨»n«/mi»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathsize=¨12px¨»c«/mi»«mi mathvariant=¨bold¨ mathsize=¨12px¨»a«/mi»«/mfrac»«mstyle mathsize=¨12px¨/»«/math»

]]> 0.0000000 0.0000000 0 4.06.5.1.11Q Resol triangle amb b i c En un triangle rectangle, els costats b i c mesuren, respectivament, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mstyle»«/math» m.
Resol el triangle.

Format: arrodonit (a la unitat). Angles en graus sense unitat

]]> 1.0000000 0.2500000 0 0 a =#sol1B =#sol2C=#sol3]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>99</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>79</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><msqrt><mrow><msup><mi>b1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>c1</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mfrac><mn>180</mn><pi/></mfrac><mo>*</mo><mi>asin</mi><mfenced><mfrac><mi>b1</mi><mi>a</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>B</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>B</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>C</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>,</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>205</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65.225</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24.775</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>C</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a es calcula amb el teorema de Pitàgores

B és l'arc sinus de #b/#a (millor fer-ho amb la hipotenusa sense arrodonir)

Per a trobar C, com que C + B = 90º, fem la resta 90º - #B.

]]> 4.06.5.1.50 TEORIA: RESOLUCIÓ AMB CATET I B

Resolució amb 1 catet i 1 angle agut

Si es coneix b i B (o C=90º-B):

es calcula a amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»sinB«/mi»«/mfrac»«/mrow»«/mstyle»«/math»
es calcula c amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tgB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»c«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»tgB«/mi»«/mfrac»«/mstyle»«/math»

Si es coneix c i C (o B=90º-C)

es calcula a amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinC«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«/mrow»«/mstyle»«/math»
es calcula b amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»tgC«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»b«/mi»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 4.06.5.1.51Q Resol triangle amb b i B. En un triangle rectangle, l'angle B mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»B_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mstyle»«/math» i el costat b mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mstyle»«/math» m.
Resol el triangle.

Escriviu els resultats arrodonits.

]]> 1.0000000 0.2500000 0 0 C =#C_1a =#a_1c =#c_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>79</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>B_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>B_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mfrac><mi>b_1</mi><mrow><mi>sin</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mfrac><mi>b_1</mi><mrow><mi>tan</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>974</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>76</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1004</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>243</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>C</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a trobar C, com que C + B = 90º, fem la resta 90º - #B_1.

]]> Per calcular a (hipotenusa) a partir de l'oposat b = #b_1, utilitzem el sinus de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mrow»«mi mathvariant=¨bold¨»sin«/mi»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfrac»«/math»

]]> Per calcular c (adjacent) a partir de l'oposat b = #b_1, utilitzem la tangent de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»c«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mrow»«mi mathvariant=¨bold¨»tg«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfrac»«/math»

]]> 4.06.5.1.52Q Resol triangle amb c i B. En un triangle rectangle, l'angle B mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»B_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mrow»«/mstyle»«/math» i el costat c mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«/mrow»«/mstyle»«/math» m.
Resol el triangle.

Escriviu els resultats arrodonits.

]]> 1.0000000 0.2500000 0 0 C =#C_1a =#a_1b =#b_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>79</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>B_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>B_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mfrac><mi>c_1</mi><mrow><mi>cos</mi><mo>(</mo><mi>r</mi><mo>)</mo></mrow></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mi>c_1</mi><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>727</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1086</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>807</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>C</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>b</mi><mi>_</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a trobar C, com que C + B = 90º, fem la resta 90º - #B_1.

]]> Per calcular a (hipotenusa) a partir de l'adjacent c = #c_1, utilitzem el cosinus de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»cos«/mi»«mo»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mi mathvariant=¨bold¨»cos«/mi»«mo»§#160;«/mo»«mi mathvariant=¨bold¨»B«/mi»«/mrow»«/mfrac»«/math»

]]> Per calcular b (oposat) a partir de l'adjacent c = #c_1, utilitzem la tangent de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»c«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»g«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«/math»

]]> 4.06.5.1.70 TEORIA: RESOLUCIÓ AMB HIPOTENUSA I B

Resolució amb la hipotenusa

i 1 angle agut

Si es coneix a i B (o C=90º-B):

es calcula b amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sinB«/mi»«/mrow»«/mstyle»«/math»
es calcula c amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cosB«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cosB«/mi»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 4.06.5.1.71Q Resol triangle amb a i B. En un triangle rectangle, l'angle B mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mrow»«/mstyle»«/math» i la hipotenusa mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«/mrow»«/mstyle»«/math» m.
Resol el triangle.

Escriviu els resultats arrodonits.

]]> 1.0000000 0.2500000 0 0 C =#c_1b =#b_1c =#c_2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>79</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>b</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>b</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a trobar C, com que C + B = 90º, fem la resta 90º - #B.

]]> Per calcular b (oposat) a partir de la hipotenusa #a, utilitzem el sinus de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«/math»

]]> Per calcular c (adjacent) a partir de la hipotenusa a, utilitzem el cosinus de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»cos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»B«/mi»«/math»

]]> 4.06.5.1.72Q Resol triangle amb a i C. En un triangle rectangle, l'angle C mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»C_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mrow»«/mstyle»«/math» i la hipotenusa mesura «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«/mrow»«/mstyle»«/math» m.
Resol el triangle.

Escriviu els resultats arrodonits.

]]> 1.0000000 0.2500000 0 0 B =#B_1b =#b_1c =#c_1]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>79</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi><mo>=</mo><mn>90</mn><mo>-</mo><mi>C_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>B_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mi>a</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>B</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>b</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>c</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Per a trobar B, com que C + B = 90º, fem la resta 90º - #C_1.

]]> Per calcular b (oposat) a partir de la hipotenusa #a, utilitzem el sinus de B:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»b«/mi»«mi mathvariant=¨bold¨»a«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sin«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»B«/mi»«/math»

]]> Per calcular c (adjacent) a partir de la hipotenusa a, utilitzem el cosinus de B:

]]> 4t ESO/4.06 TRIGONOMETRIA/4.06.5 Resolució de triangles rectangles/4.06.5.2 Problemes que fan servir les raons 4.06.5.2.61Q Problema des de dalt Des del cim d'un edifici, es veu una font situada a #c m del peu de l'edifici sota un angle de #C º. Quina és l'alçària de l'edifici?

Doneu el resultat arrodonit.

]]> 1.0000000 0.5000000 0 0 #r_63 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>89</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>C</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_63</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mfrac><mi>c</mi><mrow><mi>tan</mi><mo>(</mo><mi>C</mi><csymbol definitionURL="http://.../units/degree/angular">º</csymbol><mo>)</mo></mrow></mfrac></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>C</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>65</mn><mo>,</mo><mn>823</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>*</mo><pi/></mrow><mn>36</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_63</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>384</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#r_63</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> Cal dibuixar el triangle on l'angle C és #C º i el costat adjacent és #c.

L'angle B = 90º - #C.

I el que volem calcular és el costat oposat a B. Per a trobar el costat oposat, n'hi ha prou amb utilitzar la tangent de B

]]> 4.06.5.2.62Q Problema amb oposat Des d'un vaixell situat a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«/mrow»«/mstyle»«/math» m de la costa, es veu el cim d'un penya-segat sota un angle de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»B_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mrow»«/mstyle»«/math». Quina és l'alçada del penya-segat?

Format de la resposta: arrodonida al centèsims

]]> 1.0000000 0.5000000 0 0 #w_1 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>65</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mfrac><mrow><mi>B_1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>13</mn><mo>*</mo><pi/></mrow><mn>60</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>13.766</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml">#w_1</correctAnswer></correctAnswers><localData><data name="inputField">textField</data></localData></question> Si dibuixeu el triangle, la base és el costat c = #c, el vaixell està situat en el vèrtex de l'angle B = #B_1, i ens demanen el costat b, que és l'oposat a l'angle B.

Hem d'utilitzar la tangent que relaciona l'oposat (b) i l'adjacent (c).

]]> 4.06.5.2.64Q Problema trobar a amb B i c Una escala està recolzada a una paret. Del peu de la paret a l'escala hi ha «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«/mrow»«/mstyle»«/math» metres. Quina és la longitud de l'escala si l'angle que forma amb el terra és de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#186;«/mo»«/mrow»«/mstyle»«/math»?

Format de la resposta: arrodonida al centèsims

S'escriu que cos #B = #c/a

i per tant, a = #c/cos#B

]]> 4.06.5.2.65Q Problema trobar a amb C i b Un arbre ha quedat trencat pel vent. Ara la part trencada forma un angle de #Cº amb la part que ha quedat dreta. Quina era l'altura total de l'arbre, si la part que ha quedat dreta mesura #b m?

Format de la resposta: arrodonida al centèsims

S'escriu que cos #C = #b/a

i per tant, a = #b/cos#C.

Després, cal sumar #a i #b per saber l'altura total de l'arbre.

]]> 4.06.5.2.71Q Problema trobar B amb b i c Un edifici de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»b«/mi»«/mrow»«/mstyle»«/math» m projecta un ombra de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»c«/mi»«/mrow»«/mstyle»«/math» m. Quin angle formen els raigs de sol amb el terra en aquell moment?

Format de la resposta: angle en graus, arrodonit i sense unitats

]]>

]]> 4.06.5.2.81Q Problema amb tangents: cim Des del fons d'una vall ombrívola, veiem el cim d'un turó sota un angle de #B1 º. Si ens acostem #d m al turó, l'angle és de #B2 º. Quina és l'altura del turó?

Format de la resposta: arrodonida al centèsims

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi><mo>=</mo><mi>B1</mi><mo>+</mo><mi>M</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfrac><mrow><mi>B1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mfrac><mrow><mi>B2</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfenced close="|" open="|"><mfrac><mrow><mo>(</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r2</mi><mo>)</mo></mrow><mrow><mi>tan</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>-</mo><mi>tan</mi><mo>(</mo><mi>r2</mi><mo>)</mo></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>y</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>23</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>19</mn><mo>*</mo><pi/></mrow><mn>90</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>77</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71.57</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>

En aquest cas, d = #d.

Calculem les tangents de B1 i B2:

tg B1 = y/(x+#d)

tg B2 = y/x

Aïllem y en les dues equacions i igualem per calcular x.

Un cop calculat x en podem deduir y.

]]> 4.06.5.2.82Q Problema amb tangents Avio Dues persones es troben a un distància l'una de l'altra de #d m i observen el pas d'un avió. L'una el veu sota un angle de #B1º i l'altra sota un angle de #B2º. A quina alçada vola l'avió?

Format de la resposta: en metres arrodonida a la unitat

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi><mo>=</mo><mi>B1</mi><mo>+</mo><mi>M</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mfrac><mrow><mi>B1</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mfrac><mrow><mi>B2</mi><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfenced close="|" open="|"><mfrac><mrow><mo>(</mo><mi>d</mi><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>*</mo><mi>tan</mi><mo>(</mo><mi>r2</mi><mo>)</mo></mrow><mrow><mi>tan</mi><mo>(</mo><mi>r1</mi><mo>)</mo><mo>-</mo><mi>tan</mi><mo>(</mo><mi>r2</mi><mo>)</mo></mrow></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>y</mi><mo>)</mo></mrow><mn>100</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>23</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>23</mn><mo>*</mo><pi/></mrow><mn>180</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>38</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>19</mn><mo>*</mo><pi/></mrow><mn>90</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>77</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>71.57</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>

En aquest cas, d = #d.

Calculem les tangents de B1 i B2:

tg B1 = y/(x+#d)

tg B2 = y/x

Aïllem y en les dues equacions i igualem per calcular x.

Un cop calculat x en podem deduir y.

]]>