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 9 m from the surface of the river, then find the width of the river.

$9(\sqrt{3}+1)$

The correct answer is Option (3) → $9(\sqrt{3}+1)$

From point A, height of the bridge above the river = 9 m.

Let the distances from the foot of the bridge to the two river banks be x and y.

Using trigonometry:

Angle of depression = Angle of elevation

For 30°:

$\tan 30^\circ = \frac{9}{x} \Rightarrow x = \frac{9}{\tan 30^\circ} = 9\sqrt{3}$

For 45°:

$\tan 45^\circ = \frac{9}{y} \Rightarrow y = 9$

Width of the river:

$x + y = 9\sqrt{3} + 9 = 9(\sqrt{3} + 1)$