10. 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.
The height of both poles are equal DC = AB. The angle of elevation of of the top of the poles are and resp.
Let the height of the poles be m and CE = and BE = 80 -
According to question,
In triangle DEC,
In triangle AEB,
On equating eq (i) and eq (ii), we get
So, = 60 m
Hence the height of both poles is ()m and the position of the point is at 60 m from the pole CD and 20 m from the pole AB.