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Question

# The angles of elevation of top of a pole from two points Aand B on the horizontal line lying on opposite side of the pole are observed to be 30∘ and 60∘ If AB=100 m, then height of the pole is

A
203 m
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B
153 m
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C
103 m
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D
253 m
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Solution

## The correct option is C 25√3 mLet the height of pole be PQ=h m.And QB=d be the distance between B and foot of pole.tan60∘=hd √3=hd⇒d=h√3....(1)tan30∘=h100−d 1√3=h100−d⇒100−d=√3hSubstitute the value of d from the equation (1), we get⇒100−h√3=√3h⇒100=h(√3+1√3)⇒100=h(3+1√3)By doing cross multiplication⇒100√3=4h⇒4h=100√3⇒h=25√3 m

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