Question
Two poles of equal heights are standing opposite 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.
Solution
Let AD and BC be two poles of equal height h metres. Let P be a point on the road sucn that AP = x metres. Then BP = (80 - x) metres.
It is given that ∠APD = 60° and ∠BPC = 30°.
In right triangle APD, we have
In right triangle BPC, we have
Comparing (i) and (ii), we get
Putting this value in eq. (i), we get
And, AP = x = 20 m
BP = 80 - x = 80 - 20 = 60 mHence, height of the poles 
