Question

From the top of a building AB, 60m high angle of depression of the top and the bottom of a vertical lamp post CD are observed to be 30degree and 60degree.find . a) The horizontal distance between AB and CD b) the height of the lamp post. c) the difference between the height of the building and the lamp post.

Answer 1

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 – 3h) = 60

⇒ 180 – 60 = 3n

⇒ 120 = 3h

⇒ h = 40

Thus, the height of the tower is 40 m.
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