# 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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