From the top of the building 60m high the angle of depression of the top and bottom of a vertical lamp post are observed to be 30 degree and 60 degree respectively find

a)the distance between the building and the lamp post

b)the height of the lamp post

Let BC be the building and AD be the tower.

Let the height of tower, AD be *h* m.

Angles of depression of the top D and the bottom A of the tower CB are 30° and 60° respectively.

∴ ∠CDE = 30°

∠CAB = 60°

Since, BC = 60 m.

∴ CE = (60 – *h*) m

Let AB = DE = *x* m

In ∆DEC,

In ∆CBA,

Equating equation (1) and (2),

⇒ 3 (60 – *h*) = 60

⇒ 180 – 3*h*) = 60

⇒ 180 – 60 = 3*n*

⇒ 120 = 3*h*

⇒ *h* = 40

Thus, the height of the tower is 40 m.

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