Question

A T.V. tower stands vertically on a bank of a river 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

Let AB be the T.V tower of height ‘h’ m on the bank of river and ‘D’ be the point on the opposite side of the river. An angle of elevation at the top of the tower is 30°

Let AB = h and BC = x

And, given CD = 20 m

From fig. we have

In ΔACB

h = 10√3 m

And,

x = h/√3

x = 10√3/ √3

x = 10

Therefore, the height of the tower is 10√3 m and width of the river is 10 m.