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<quiz>
  <question type="stack">
    <name>
      <text>5.1.9 (Sine rule find length 2)</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<p>Suppose that we have a triangle of the following form.</p>
<p><img style="display: block; margin-left: auto; margin-right: auto;" src="@@PLUGINFILE@@/Sine%20Rule.png" alt="sine rule triangle" width="534" height="296" />

<p>Suppose that length \(BC = {@BC@}\)cm, angle \(A = {@aa@}^\circ\), angle \(C = {@cc@}^\circ\) find the length of the side \(AB\). Give your answer to the nearest centimetre.</p>
<ul style="list-style: none;">
<li>AB = [[input:ans1]] [[validation:ans1]] cm</li>
</ul>]]></text>
<file name="Sine Rule.png" path="/" encoding="base64">[encoded data, 68868 characters]</file>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<p>Here we use the sine rule. Recall that 
\[ 
\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c} \qquad \mbox{ or } \qquad \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}. 
\]
So in this case we have that angle \(A = {@aa@}\), angle \(C = {@cc@}\) and \(BC = a = {@BC@}\). Thus inputting into the sine rule we have 
\[
\frac{AB}{\sin {@cc@}^\circ} = \frac{{@BC@}}{\sin {@aa@}^\circ} \implies AB = \left( \frac{{@BC@}}{\sin {@aa@}^\circ}\right) \cdot \sin{@cc@}^\circ \approx {@ta1@} \: cm.
\]</p>]]></text>
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    <idnumber/>
    <stackversion>
      <text>2020081700</text>
    </stackversion>
    <questionvariables>
      <text>sind(d):=sin(d*%pi/180);
asind(x)=asin(x)*180/%pi;

aa: 30 + rand(10);
bb: 1;
cc: 50+ rand(10);

BC: 10+rand(5);
AC: 1;
AB: (BC/(sind(aa)))*sind(cc);

ta1: round(AB);</text>
    </questionvariables>
    <specificfeedback format="html">
      <text><![CDATA[<p>[[feedback:prt1]]</p>]]></text>
    </specificfeedback>
    <questionnote format="moodle_auto_format">
      <text>\(AB = \left( \frac{{@BC@}}{\sin {@aa@}}\right) \cdot \sin{@cc@} \approx {@ta1@}\)</text>
    </questionnote>
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      <text/>
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      <text><![CDATA[<p>Correct answer, well done.</p>]]></text>
    </prtcorrect>
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      <text><![CDATA[<p>Your answer is partially correct.</p>]]></text>
    </prtpartiallycorrect>
    <prtincorrect format="html">
      <text><![CDATA[<p>Incorrect answer.</p>]]></text>
    </prtincorrect>
    <decimals>.</decimals>
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      <type>algebraic</type>
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  </question>
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