A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff of height 5 metres. At a point on the plane, the angles of elevation of the bottom and the top of the flag-staff are respectively 30° and 60°. Find the height of the tower.

Let the height of the tower = h (m)

Let the point of elevation on the ground is (m) away from the foot of the tower.

In ∆DBC,

tan 30° =

=

On the cross multiplication

= h√3 -------(1)

In ∆ABC,

tan 60° =

√3 =

√3 = ---------(2)

On substituting value of from equn. (1) in eqn. (2)

√3 =

h√3×√3 = 5+h

3h = 5+h

3h-h = 5

2h = 5 ⇒ h =

h = 2.5 m.

Therefore height of the tower is 2.5 m.