Question

From a point on a bridge across a river the angles of depression of the banks on opposite sides of the river are ${30}^{\circ }$ and ${45}^{\circ }$ respectively. If the bridge is at a height of 6 m from the banks find the width of the river.

• A. 6 m
• B. 6√3 m
• C. 3√3 m
• D. 6+ 6√3 m

Answer 1

The correct option is D

6+ 6√3 m

If the line through P is the bridge

In $\Delta$PDA, $\angle$A = ${30}^{\circ }$

PD = 6

AD = PD $\sqrt{3}$ = 6$\sqrt{3}$

In $\Delta$PDB, $\angle$B = ${45}^{\circ }$

DB = PD = 6

Hence width of the river = 6 + 6$\sqrt{3}$ = 6(1+$\sqrt{3}$) m