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}'' 
 


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xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q_41&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_42&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mi&gt;t_41&lt;/mi&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_44&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;quocient&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;q_41&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m_42&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;t_42&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;residu&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mfenced&gt;&lt;mi&gt;q_41&lt;/mi&gt;&lt;/mfenced&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m_42&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q_42&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;a_43&lt;/mi&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;mn&gt;60&lt;/mn&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;mi&gt;t_42&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_45&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;quocient&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;q_42&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m_42&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_46&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;residu&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;q_42&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;m_42&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;d_41&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;40&lt;/mn&gt;&lt;mo&gt; &lt;/mo&gt;&lt;csymbol definitionURL=&quot;http://.../units/degree/angular&quot;&gt;°&lt;/csymbol&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;mo&gt; &lt;/mo&gt;&lt;csymbol definitionURL=&quot;http://.../units/minute/angular&quot;&gt;&amp;apos;&lt;/csymbol&gt;&lt;mo&gt; &lt;/mo&gt;&lt;mn&gt;54&lt;/mn&gt;&lt;mo&gt; &lt;/mo&gt;&lt;csymbol definitionURL=&quot;http://.../units/second/angular&quot;&gt;&amp;apos;&amp;apos;&lt;/csymbol&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;m_42&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;8&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_43&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;5&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;t_41&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q_41&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_44&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;t_42&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;4&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;q_42&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;294&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_45&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;36&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_46&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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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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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;45&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;44&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;s_31&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;180&lt;/mn&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;/session&gt;</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>&nbsp;</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, °, ', &quot;</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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;89&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;90&lt;/mn&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;89&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;89&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;90&lt;/mn&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;6&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;84&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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)

]]> 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>B</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>35</mn><mo>,</mo><mn>65</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B1</mi><mo>=</mo><mi>B</mi><mo>*</mo><mfrac><pi/><mn>180</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></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>a</mi><mo>=</mo><mfrac><mi>b1</mi><mrow><mi>sin</mi><mo>(</mo><mi>B</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></mfrac></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>10</mn><mo>*</mo><mi>a</mi><mo>)</mo></mrow><mn>10</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>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>52</mn></math></output></command><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>4</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>5.1</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>5.0761</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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer dibuixes dos eixos perpendiculars. 

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)

]]> 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>C</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>35</mn><mo>,</mo><mn>65</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>C</mi></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>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></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>a</mi><mo>=</mo><mfrac><mi>c1</mi><mrow><mi>cos</mi><mo>(</mo><mi>B</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></mfrac></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>10</mn><mo>*</mo><mi>a</mi><mo>)</mo></mrow><mn>10</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>63</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>27</mn></math></output></command><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>4</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>4.5</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>4.4893</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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer dibuixes dos eixos perpendiculars. 

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)

]]> 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>C</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>35</mn><mo>,</mo><mn>65</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>C</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>8</mn><mo>)</mo></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>b</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>B</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></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>10</mn><mo>*</mo><mi>b</mi><mo>)</mo></mrow><mn>10</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>44</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>46</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.3</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>4.316</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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer dibuixa una recta i a la dreta de la recta marca el vèrtex B

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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;c&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;15&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;44&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msqrt&gt;&lt;mn&gt;2161&lt;/mn&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;29&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;22&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msqrt&gt;&lt;mn&gt;357&lt;/mn&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;apply&gt;&lt;csymbol definitionURL=&quot;http://www.wiris.com/XML/csymbol&quot;&gt;repeat&lt;/csymbol&gt;&lt;mtable&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mn&gt;11&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;49&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mtd&gt;&lt;/mtr&gt;&lt;mtr&gt;&lt;mtd/&gt;&lt;/mtr&gt;&lt;/mtable&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;&amp;gt;&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;/mrow&gt;&lt;/apply&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msqrt&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;msup&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msup&gt;&lt;/mrow&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;29&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;22&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;r_61&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;msqrt&gt;&lt;mn&gt;357&lt;/mn&gt;&lt;/msqrt&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</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, 

#D

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.

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