WAEC 2020 · Paper 1 · Q24

In the diagram, $XYZ$ is an equilateral triangle of side $6\text{ cm}$ and $T$ is the midpoint of $XY$ . Find $\tan(\angle XZT)$ .

Worked solution (try it first)

Every angle of an equilateral triangle is $60^\circ$ , so $\angle XZY = 60^\circ$ .
$ZT$ goes from $Z$ to the midpoint of $XY$ , so it is a line of symmetry and cuts the angle at $Z$ in half: $\angle XZT = 30^\circ$ .
So $\tan(\angle XZT) = \tan30^\circ$
$= \frac{1}{\sqrt3}$ , option A.