JAMB 2012 · UTME · Q36

Elevation, depression & bearings

A man stands on a tree $150\text{ cm}$ high and sees a boat at an angle of depression of $74^\circ$ . Find the distance of the boat from the base of the tree.

Worked solution (try it first)

The angle of elevation of the man from the boat is also $74^\circ$ (alternate angles), so $\tan74^\circ = \frac{150}{d}$ .
Rearrange: $d = \frac{150}{\tan74^\circ}$
$= \frac{150}{3.487}$ .
So $d \approx 43$ cm, option B.

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