Q) From a point on a bridge across the river, the angles of depressions of the banks on opposite sides of the river are 30° and 60° respectively. If the bridge is at a height of 4 m from the banks, find the width of the river.

Ans: 

Let’s start with a diagram for this given question:

Step 1: Let’s start with Δ ARP,

tan R =

since AP = 4 m (given)

∴ tan 60 =

∴ √3 =

∴ AR =

∴ AR = ……….. (i)

Step 2: Next, let’s look at Δ BRQ,

tan R =

since BQ = 4 m (given)

∴ tan 30 =

∴

∴ BR = 4 √3 ……….. (ii)

Step 3: Next, from the diagram, we have:

Width of the river, AB = AR + BR

By substituting values of AR from equation (i) and value of BR from equation (ii)

AB =

AB =

AB =

AB = m

By substituting √3 = 1.73, we get:

AB = = 9.23 m

Therefore, the width of the river is 9.23 m

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