JAMB 1995 · UME · Q34

In the diagram, $PR = 10$ cm and $\angle QPR = 30^\circ$ . Find $PQ$ if the area of triangle $PQR$ is $35\text{ cm}^2$ .

Worked solution (try it first)

Use area $= \frac12ab\sin C$ with the $30^\circ$ angle between $PQ$ and $PR$ : $\frac12 \times PQ \times 10 \times \sin30^\circ = 35$ .
$\sin30^\circ = \frac12$ , so the left side is $2.5 \times PQ$ .
So $PQ = 35 \div 2.5 = 14$ cm, option C.