From a point 20 m away from the foot of a tower, the angle of elevation of thetop of the tower is 30 ^ยบ. Find the height of the tower.

Given:

Distance of the point from the foot of the tower, d = 20m

Angle of elevation, θ = 30°

To find: Height of the tower, AB

Let AB be the height of the tower and C be the point.

In right angled Δ ABC,

tan [θ] = Opposite / Adjacent

Here θ = 30°

And also the opposite side is AB and the adjacent side is BC

∴ tan 30 ^o = AB/BC

AB = BC tan 30°

From the question we know that BC = d = 20m

= 20 × (1 /√ 3) m

= 20 × 0.57735

= 11.56 m

Therefore the height of the tower is 11.56 m.