Question

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point between them on the road the angles of elevation of the top of the poles are 60° and 30° respectively. Find the height of the poles and the distances of the point from the poles.

Answer 1

Let AB and ED are two poles of equal height.

Let C be the point between the poles on the ground. 

Since poles are vertical to the ground.∠ADC = ∠ABC = 90°In a right-angled triangle, we know,

√3h = 80 - x----------(2) 

On substituting value of h from eqn.(1) in eqn. (2) 

√3 × √3x = 80 - x 

⇒ 3x = 80 - x 

⇒ 4x = 80 

⇒ x = 20 m 

On substituting value of x in eqn. (1) 

h = 20√3Distance of C from pole ED = 20 m Distance of C from pole AB = 80 - 20 = 60 m 

Therefore the height of the poles is 20√3 m. and distances of the points from one pole is 20 m and from other pole is 60 m.