Q27 of 107 Page 12

A T.V. tower stands vertically on a bank of a river. From a point on the other bank directly opposite the tower, the angle of elevation of the top of the tower is 60°. From a point 20 m away this point on the same bank, the angle of elevation of the top of the tower is 30°. Find the height of the tower and the width of the river.

Let BC be the height of the T.V tower and AB be the width of the river.


In ∆ABC,


tan 60° =


√3 = ------(1)


In ∆ABC,


tan 30° =


tan 30° =


=


√3h = 20+ ---------(2)


On substituting value of h in eqn.(2)



√3× √3 = 20+


3


3


2



On substituting value of in eqn. (1)


h = √3


h = 10√3 m.


Therefore height of T.V tower is 10√3 m. and width of river is 10 m.


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