1MA 01. TRIGONOMETRIA/1MA.01.1 Raons 1MA.01.1.11Q Semblança triangles Els dos triangles són semblants.

Els costats mesuren: a=#a, b = #b, d = #d i f = #f

Calcula:

a) la proporció (raó de semblança) entre el triangle gran i el petit.

b) c

c) e

]]> 1.0000000 0.5000000 0 0 1. r =#sol2. c =#c3. e =#e]]> <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>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>29</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><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>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>49</mn><mo>)</mo></mtd></mtr><mtr><mtd><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><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>f</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mi>r</mi></mtd></mtr><mtr><mtd><mi>i_1</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>r</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>></mo><mi>c</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>+</mo><mi>c</mi><mo>></mo><mi>b</mi></mrow></mfenced><mo>∧</mo><mo>(</mo><mi>b</mi><mo>+</mo><mi>c</mi><mo>></mo><mi>a</mi><mo>)</mo></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo> </mo><mi>c</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mspace linebreak="newline"/><mn>3</mn><mo>.</mo><mo> </mo><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</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> Primer calculem la raó d/a = #r_1 que ens dona la proporció entre el triangle gran i el triangle petit (el triangle gran és #r_1 vegades més gran que el petit).
Com que són semblants,
per calcular c (en el petit), dividim f = #f (del gran)per #r_1;
per calcular e (del gran), multipliquem b = #b (del petit) per #r_1

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