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Question

A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b feet just above A is β. Then, the height of the tower is


A

btan(α)cot(β)

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B

bcot(α)tan(β)

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C

bcot(α)cot(β)

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D

btan2(α)cot(β)

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Solution

The correct option is A

btan(α)cot(β)


Finding the height of the tower:

Given, A tower subtends an angle α at a point A in the plane of its base and the angle of depression of the foot of the tower at a point b feet just above A is β.

Assume ‘X’ is the distance from point ‘A’ to foot of the tower.

Let ‘h’ be the height of the tower h=PQ

In APQ,

h=xtan(α).....(i)

In PRB

b=xtan(β)x=btan(β)x=bcot(β)...(ii)

From equation (i)&(ii)

h=btan(α)cot(β)

Hence, correct option is (A).


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