JAMB 1994 · UME · Q37

The angle of depression of a boat from the top of a cliff 10 m high is $30^\circ$ . How far is the boat from the foot of the cliff?

Worked solution (try it first)

The angle of elevation of the cliff top from the boat is also $30^\circ$ (alternate angles).
So $\tan30^\circ = \frac{10}{d}$ , giving $d = \frac{10}{\tan30^\circ}$ .
Dividing by $\frac{1}{\sqrt3}$ multiplies by $\sqrt3$ : $d = 10\sqrt3$ m, option C.