JAMB 1997 · UME · Q37

Sine & cosine rules

In the figure, $XYZ$ is a triangle with $XY = 5$ cm and $XZ = 2$ cm; $XZ$ is produced to $E$ , making $\angle YZE = 150^\circ$ . If $\angle XYZ = \theta$ , calculate $\sin\theta$ .

Worked solution (try it first)

Angles on a straight line add up to $180^\circ$ , so $\angle XZY = 180^\circ - 150^\circ$
$= 30^\circ$ .
Sine rule: $XZ = 2$ faces $\theta$ and $XY = 5$ faces the $30^\circ$ at $Z$ .
So $\dfrac{\sin\theta}{2} = \dfrac{\sin30^\circ}{5}$ .
So $\sin\theta = \dfrac{2 \times \frac12}{5}$
$= \frac15$ , option D.

Report a problem with this question