**Q) **From a point on a bridge across a river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 3 m from the banks, then find the width of the river.

**A****ns:**

**Step 1: Diagram for this question:**

**Step 2: Calculation for the bridge length on LHS:**

Let ‘s start with Δ ARB,

tan ∠ ARB =

∴ tan 45° =

∴ D_{1} = 3 ……….. (i)

**Step 3: Calculation for the bridge length on RHS:**

Next in Δ BRQ,

tan ∠ BRQ =

∴ tan 30° =

∴

∴ D_{2 } = 3√3 ….. (ii)

**Step 4: Combining the results:**

Since, Width of the river = Bridge length AB = AR + BR = D_{1 }+ D_{2}

From equations (i) and (ii), we get:

AB = 3 + 3√3 = 3 (√3 + 1) m

**Therefore, the width of the river is 3(√3 + 1) m. **