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.
Height of the poles = 20 m
Distances of the point from the poles = 20 m and 60 m
Explanation
This is a standard heights and distances problem from NCERT Class 10. The key insight is that since both poles have equal heights, we can set up two trigonometric equations using tan of the given angles and equate them. The total distance (80 m) equals the sum of distances from the point to both poles, which allows us to solve for the unknown distance and subsequently the height.