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      <text>5.1.14 (Cosine rule example)</text>
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      <text><![CDATA[<h3>Example</h3>

<p> Suppose that we have a triangle \(ABC\) where \(AB = 5\)cm, \(BC=3cm\) and angle \(B = 50^\circ\). Find the length of the remaining side of the triangle.</p>

<h3>Solution</h3>

<p>Note that the remaining side of the triangle is the side \(AC\) which corresponds to the symbol \(b\) in the cosine rule. Thus from the cosine rule we have 
\[
b^2 = a^2 + c^2 - 2ac\cos B.
\]
In this case we have \(a = 3, c = 5\) and \(B = 50^\circ\), so substituting these into the above equation we obtain
\[
AC^2 = b^2 = 3^2 + 5^2 - (2 \cdot 3 \cdot 5 \cdot \cos 50^\circ) = 34 - 30 \cdot 50^\circ \approx 14.7 \: \mbox{cm}.
\]</p>]]></text>
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