Q. 94.2( 19 Votes )

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.

Answer :

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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