A tower subtends an angle a 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

1) b tan α cot β

2) b cot α tan β

3) b cot α cot β

4) b tan2 α cot β

Solution: (1) b tan α cot β

JEE Questions Q31

Assume x to be the distance of point A from the foot of the tower.

Also, h be the height of the tower.

In △APQ,

h = x tan α … (i)

In △PRB

b = x tan β … (ii)

From (i) and (ii),

h = b . tan α / tan β = b . tan α cot β

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