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Question

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be α. After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to β. Then the height (in metres) of the tower is :

A
cos(βα)sinαsinβ
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B
2sin(βα)sinαsinβ
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C
2sinαsinβsin(βα)
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D
sinαsinβcos(βα)
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Solution

The correct option is D 2sinαsinβsin(βα)
Ltanα=h

(L2)tanβ=h
htanα=htanβ+2
h=2tanαtanβtanβtanα=2sinαcosα×sinβcosβsinαcosβcosαsinβcosαcosβ=2sinαsinβsin(βα)

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