Question

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

Answer 1

A and B represent points on the bank on opposite sides at the river, so that AB is the width of the river. P is a point on the bridge at a height of 3m i.e., DP = 3 m. We are interested to determine the width at the river which is the length at the side AB of the ΔAPB.

Now, AB = AD + DB

Also, in right ΔPBD,

B = 45°

So, BD = PD = 3 m

Now, AB = BD + AD

= 3 + 3√3 = 3(1 + √3)m

Therefore, the width at the river is 3(√3 + 1)