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.

Let AB and DE be the poles and BD be the road.

In ΔABC, tan60° = AB/BC
BC = AB/√3
AB = √3 BC .. (i)

In ΔDEC, tan30° = DE/CD
→ DE/(80 - BC) = 1/√3
AB = DE .. (poles of same height)
→ √3 BC/(80 - BC) = 1/√3 [From (i)]
→ 3BC = 80 - BC
→ 4BC = 80
→ BC = 20m

Therefore, height of the poles = 20√3 m
Distance of the point from the poles are 20m and 80 - 20 = 60m respectively.