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 BD is 80m wide road and AB and CD are the two equal poles.
Let AB = CD = x
In ΔABO,
AB/BO = tan 60° ⇒ x/BO = √3 ⇒ BO = x/√3
In ΔCDO,
CD/DO = tan 30° ⇒ x/(80-BO) = 1/√3 ⇒ x√3 = 80 – BO
⇒ x√3 = 80 – x/√3 [Putting the value of BO]
⇒ x√3 + x/√3 = 80 ⇒ 3x + x = 80√3 ⇒ 4x = 80√3 ⇒ x = 20√3
Therefore, BO = x/√3 = 20√3/√3 = 20
DO = BD – BO = (80 – 20) m = 60 m
Hence, the height of pole is 20√3 m and distance of poles from the point is 20m and 60m.