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.
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