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From the top of a cliff 92 m high, the angle of depression of a buoy is 20°. Calculate, to the nearest metre, the distance of the buoy from the foot of the cliff.

Heights & Distances

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Answer

Let AB be the cliff and C be the buoy.

A man stands 9 m away from a flag-pole. He observes that angle of elevation of the top of the pole is 28° and the angle of depression of the bottom of the pole is 13°. Calculate the height of pole. Heights and Distances, Concise Mathematics Solutions ICSE Class 10.

Given,

AB = 92 m

From figure,

In △ACB,

tan 20°=PerpendicularBase⇒tan 20°=ABBC⇒0.364=92BC⇒BC=920.364⇒BC=252.7≈253 meters.\text{tan 20°} = \dfrac{\text{Perpendicular}}{\text{Base}} \\[1em] \Rightarrow \text{tan 20°} = \dfrac{AB}{BC} \\[1em] \Rightarrow 0.364 = \dfrac{92}{BC}\\[1em] \Rightarrow BC = \dfrac{92}{0.364} \\[1em] \Rightarrow BC = 252.7 ≈ 253 \text{ meters}.

Hence, the distance of the buoy from the foot of the cliff is 253 meters.

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