The angle of elevation of the top of a hill at the foot of a tower is 60ºand the angle of elevation of top of the tower from the foot of the hillis 30º. If the tower is 50 m high, what is the height of the hill?

Question

Philoid · Accepted Answer

Given:

Height of the tower, h = DC = 50 m

Angle of elevation of a hill at the foot of tower, θ = 60°

Angle of elevation of top of tower from foot of the hill, ϕ = 30 °

To find: Height of the hill

Solution:

Let h be the height of the hill and x m be the distance between the foot of the hill and foot of the tower.

In right angled Δ ABC,

cos 60 ^o = x / h

x = h cot 60 ^o …………… (i)

In right angled Δ DBC,

cot 30 ^o = x / 50

x = 50 cot 30 ^o …………… (ii)

Equating (i) and (ii)

h cot 60° = 50 cot 30°

h = 50 cot 30° / cot 60°

= 50 × 3

= 150 m

Therefore the height of the hill is 150 m.