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    <name>
      <text>5.1.7 (Sine rule example)</text>
    </name>
    <questiontext format="moodle_auto_format">
      <text><![CDATA[<h3>Example</h3>

<p>Suppose that we have a triangle \(ABC\) as above. Let angle \(A = 48^\circ\), angle \(C = 78^\circ\) and the length of side \(AB\) be \(23\)cm. Hence find the length of side \(BC\).</p>

<h3>Solution</h3>

<p>Substituting the values into the sine rule and noting that \(BC = a\) we have that
\[
\frac{a}{\sin A} = \frac{23}{\sin 37^\circ} \implies \frac{a}{\sin 48^\circ} = \frac{23}{\sin 37^\circ}.
\]
Hence, we can rearrange this expression so that we get the length \(a\);
\[
a = \sin 48^\circ \times \left(\frac{23}{\sin 37^\circ}\right) \approx 28.4\: cm
\]</p>]]></text>
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