Two poles of equal heights are standing opposite each other on either side of the roads, 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 the height of the poles be h.
Then AB = ED = h
BD = 80m [given]
Let the given point be C such that BC = x and CD = 80 - x
In △ABC, tan30° = AB/BC → 1/√3 = h/x → x = √3h
In △ECD, tan60° = ED/CD → √3 = h/(80 - x) → h = (80 - x)√3
Put the value x = √3h we get
h = (80 - √3h)√3 → h = 80√3 - 3h → 4h = 80√3 → h = 20√3
Then, height of poles h = 20√3m