JAMB 1992 · UME · Q35

In the figure, $\angle XZY = 90^\circ$ , $XZ = 10$ cm, $\angle ZXR = 30^\circ$ and $\angle RXY = 15^\circ$ . Calculate $RY$ in cm.

Worked solution (try it first)

The whole angle $ZXY$ is $30^\circ + 15^\circ = 45^\circ$ .
In the right-angled triangle $XZY$ : $ZY = 10\tan45^\circ = 10$ cm.
In the right-angled triangle $XZR$ : $ZR = 10\tan30^\circ = \frac{10}{\sqrt3}$ cm.
$R$ lies on $ZY$ , so $RY = ZY - ZR$
$= 10 - \frac{10}{\sqrt3}$
$= 10\left(1 - \frac{1}{\sqrt3}\right)$ cm, option B.