Question

From a point on a bridge across a river, the angles of depression of the banks on opposite side of the river are 30° and 45°, respectively. If the bridge is at height of 4 m from the bank, find the width of the river.

Answer 1

Given : Height of bridge from river

AO = 4 m

BO = x, CO = y

From right angled ∆AOB

AO/BO = tan 45°

⇒ 4/x = 1

⇒ x = 4 m ……(i)

Again from right angled ∆AOC,

AO/CO = tan 30°

⇒ 4/y = 1/√3

⇒ y = 4√3 m ……(ii)

From equation (i) and (ii)

Width of river = x + y

= 4√3 + 4

= 4(√3 + 1)

= 4(1.732 + 1)

= 4(2.732)

= 10.92 m

Hence, width of river is 10.92 m