waecmaths question:
From the top of a vertical cliff 20m high, a boat at sea can sighted 75 m away and on the same horizontal position 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
Option A:
56o
Option B:
75o
Option C:
16o
Option D:
15o
waecmaths solution:
$\text{The angle of depression by }\angle ABC$
$\angle ABC=\theta$
$\angle BDC=\angle ABC=\theta \text{ }\!\!\{\!\!\text{ Alternate angles }\!\!\}\!\!\text{ }$
$\tan \theta =\frac{opp}{adj}=\frac{BC}{DC}$
$\tan \theta =\frac{20m}{75m}=0.2667$
$\theta =14.9{}^\circ$
$\theta \approx 15{}^\circ$
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