A vertical tower stands on a horizontal plane and is surmounted by a flag-staff of height 7 m. From a point on the plane, the angle of elevation of the bottom of the flag-staff is 30° and that of the top of the flag-staff is 45°. Find the height of the tower.
Let the height of tower is BD = h (m.)
Now in ∆ABC
tan 45° = ⇒
1 =
7+h = ------(1)
Now in ∆DBC
tan 30° =
=
----------(2)
On substituting value of in eqn.(1)
7+h = √3h
√3h- h = 7
h (√3-1) = 7
h = ⇒
= 9.56m.
Therefore height of tower is 9.56m.