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.
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