Two poles of equal heights are standing opposite each other on either side of the road, which is 90 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.
The above figure represents the situation given in the question
tan30∘=ABBC⇒tan30∘=ABx⇒x√3=AB……(1)tan60∘=EDCD⇒√3=ED90−x⇒√3(90−x)=ED……(2)But ED=AB, therefore from eq(1) and (2)√3(90−x)=x√3⇒=270−3x=x⇒x=67.5m∴AB=67.5√3=39m (approx) which is the height of the poles