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Question

# A man lying on a 6 m tall building finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

A
63 m
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B
6 m
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C
23 m
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D
33 m
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Solution

## The correct option is A 6√3 m Given: Man is at a height of 6 m. Height of the building = 24 m. Angle of elevation and angle of depression are complementary angles. To find: Distance between man and the pillar EC. Since the height of the building is 6m, AE = BC = 6 m. Remaining height of the pillar = 24 m - 6 m = 18 m So, BC = 18 m. If the angle of depression is ∠CEB=θ, then the angle of elevation will be ∠CED=90o−θ. The trigonometric ratio connecting the oposite side and adjacent side is tan θ. Hence, in triangle ECB, tan θ=BCEC=6EC-----(i) Similarly, in triangle ECD, tan(90−θ)=cotθ=ECDC=18EC------(ii) We know that, tanθ=1cotθ⇒6EC=118EC⇒6EC=EC18⇒EC2=108 Taking square root on both the sides, we get EC=6√3 m The distance of man from the pillar is 6√3 m.

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