Question

The angle of elevation of the top of a pillar from a point on the ground is 15° on walking 100 m towards the tower, the angle of elevation is found to be 30°. Calculate the height of the tower (where tan 15 = 2 – √3).

Answer 1

Let CD is a pillar of height h m. The angle of elevation of its top at A be 15°. 

Let B be a point at a distance of 100 m from A such that the angle of elevation of the top of the tower at B be 30°.

Let BC = x m, 

so ∠DAC = 15°, ∠DBC = 30°, AB = 100 m

From right angled ∆BCD,

tan 30° = CD/BC

⇒ 1/√3 = h/x

⇒ x = h√3 m

From right angled ∆ACD,

Hence, height of pillar is 50 m