WAEC 2019 · Paper 1 · Q37

Elevation, depression & bearings

From the top of a vertical cliff $20\text{ m}$ high, a boat at sea can be sighted $75\text{ m}$ away on the same horizontal level as the foot of the cliff. Calculate, correct to the nearest degree, the angle of depression of the boat from the top of the cliff.

Worked solution (try it first)

The angle of depression equals the angle of elevation of the cliff top from the boat (alternate angles).
The height 20 m is opposite the angle and 75 m is adjacent: $\tan\theta = \frac{20}{75}$ .
So $\theta = \tan^{-1}0.2667$
$\approx 14.9^\circ$ , which is $15^\circ$ to the nearest degree, option D.

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