Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point in between them on the road, the angles of elevation of the top of poles are 60º and 30º respectively. Find the height of the poles and the distances of the point from the poles.

### Answer

In ∆ABC,

h/x = tan 60°

⇒ h = x√3

ln ∆ECD,

h/(80 – x) = tan 30°

⇒ hx√3 = 80 – x

x√3 × √3 = 80 – x

⇒ x = 20

∴ h = 20x√3

∴ height of poles 20x√3 m

Distances of poles from the point are 20 m and 60 m.