JAMB 1995 · UME · Q36

$QRS$ is a triangle with $QS = 12$ m, $\angle RQS = 30^\circ$ and $\angle QRS = 45^\circ$ . Calculate the length of $RS$ .

Worked solution (try it first)

Sine rule: $RS$ faces the $30^\circ$ at $Q$ , and $QS = 12$ faces the $45^\circ$ at $R$ .
So $\dfrac{RS}{\sin30^\circ} = \dfrac{12}{\sin45^\circ}$ .
So $RS = \dfrac{12 \times \frac12}{\frac{\sqrt2}{2}}$
$= \dfrac{12}{\sqrt2}$ .
Rationalise: $\dfrac{12\sqrt2}{2} = 6\sqrt2$ m, option C.