Mathematics
A vertical tower is 20 m high. A man standing at some distance from the tower knows that the cosine of the angle of elevation of the top of the tower is 0.53. How far is he standing from the foot of the tower ?
Heights & Distances
ICSE
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Answer
Let θ be the angle of elevation,
Given, cos θ = 0.53
∴ cos θ = cos 58°
⇒ θ = 58°
Let MP be the vertical tower and the man be standing at point O.
Considering △POM,
∠PMO = 90°, ∠POM = 58° and MP = 20 m.
From △POM, we get
Hence, the man is at a distance of 12.5 metres from the foot of tower.
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