WAEC 2019 · Paper 1 · Q23

In $\triangle XYZ$ , $|YZ| = 32\text{ cm}$ , $\angle YXZ = 52^\circ$ and $\angle XZY = 90^\circ$ . Find, correct to the nearest centimetre, $|XZ|$ .

Worked solution (try it first)

$YZ = 32$ cm is opposite the $52^\circ$ angle at $X$ , and $XZ$ is adjacent to it, so use tangent: $\tan52^\circ = \dfrac{32}{XZ}$ .
Rearrange: $XZ = \dfrac{32}{\tan52^\circ}$
$= \dfrac{32}{1.280}$
$\approx 25.0$ .
To the nearest centimetre, $XZ = 25$ cm, option B.