Question

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.

Answer 1

Given :

Distance CD = 20m

Let us take the height of the tower be AB.

And BC be the width of the river.

Now in ΔABD ,

tan 30° = AB/ BD => BD = AB √3

Now in  ΔABC,

tan 60° = AB/BC => BC = AB/√3

and since , CD = 20 = BD - BC =  AB √3 - AB/√3 = 20

=> 2AB = 20√3

AB = 10 √3 = 10 * 1.732 = 17.32 m

Therefore, height of the tower is 17.32 m

and width of the river BC = 10√3 / √3 = 10m