Question

From a point on the ground the angle of elevation of the bottom and top of a transmission tower fixed at the top of 20 m high building are 45° and 60° respectively. Find the height of the transmission tower.

Answer 1

Given,

Height of the building = 20 m = AB

Let height of tower above building = h = BC

Height of tower + building = (h + 20) m [from ground] = CA

Angle of elevation of bottom of tower, α = 45°

Angle of elevation of top of tower, β = 60°

Let distance between tower and observation point = x m

Then, from the fig. we have

h = 20(1.73 − 1) = 20 x .732 = 14.64

Therefore, the height of the tower is 14.64 m.