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Height and Distance
Height and Distance
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Question

A pole stands vertically inside a triangular park ABC. Let the angle of elevation of the top of the pole from each corner of the park be π3{\pi \over 3}. If the radius of the circumcircle of Δ\DeltaABC is 2, then the height of the pole is equal to :

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Solution

Let PD = h, R = 2 As angle of elevation of top of pole from A, B, C are equal. So D must be circumcentre of Δ\DeltaABC tan⁡(π3)=PDR=hR\tan \left( {{\pi \over 3}} \right) = {{PD} \over R} = {h \over R} h=Rtan⁡(π3)=23h = R\tan \left( {{\pi \over 3}} \right) = 2\sqrt 3

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