Q. 344.2( 18 Votes )

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.

Answer :

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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