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 P between them on the road, the angle of elevation of the top of one pole is 60° and the angle of depression from the top of another pole at P is 30°. Find the height of each pole and distances of the point P from the poles.

Question

Philoid · Accepted Answer

Let AD and BC be the two poles of equal height standing on the two sides of the road of width 80 m. Join DC. Then DC = 80 m. P is a point on the road from which the angle of elevation of the top of tower AD is 60°. Also, the angle of depression of the point P from the point B is 30°. Draw a line BX from B parallel to the ground. Then ∠XBP = ∠BPC = 30°. We are to find the height of the poles and the distance of the point P from both the poles. Also, ∠APD = 60°.

Let DP = x. Then PC = 80-x.

In ∆APD,

or,

Now, from ∆APD,

or,

Now, BC = AD

So,

or,

x = 20 m

So,PD = 20 m. Hence, PC = 80-20 = 60 m. Also, BC = AD = 20√3 m.