Question

# Two poles of different heights are erected from the ground. If the smaller pole is 20 m high and distance between two poles are 10 m, and the angle of elevation of the top of the longer pole from that of the shorter pole is 60∘, find the length of the second pole.

A

20+103 m

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B

20+53 m

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C

10+103 m

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D

20+103 m

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Solution

## The correct option is D 20+10√3 m Distance between the two poles, AC=10 m Height of the shorter pole, AE=CD=20 m Let BC=x m Consider the right angled triangle ABC, tan60∘=opposite sideadjacent side=BCAC=x10 ⇒x=10×tan60∘ ∵tan60∘=√3 ∴x=10√3 m Thus, height of second pole =CD+BC=20+10√3 m

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