Question

From a point on the roof of a building 22 mt. height it is observed that the angles of depression of the top and foot of a lamp post are 30 degree and 60 degree respectively . what is the height of the lamp post ?​

Answer 1

Answer:

Height of the lamp post be l metres (say).

Let, foot of the lamp post be d metres away from the foot of the building.

So, tan 60° = (√3) = (22 / d)

or, d = (22 / √3)

Now, tan 30° = (1 / √3) = (22 - l) / d

or, (22 - l) = d * (1 / √3) = (22 / 3)

l = 22 - (22 / 3) = (44 / 3)

l ≈ 14.667

Height of the lamp post ≈ 14.667 ft.