A bridge built across a river makes an angle of 45° with the river bank as shown in given figure. If the length of the bridge is 150 m, then what is the width of the river?

Correct option is B

Given:

Length of the bridge = 150 m

Angle of the bridge with the riverbank = $$45^\circ$$​​

We need to find the width of the river (perpendicular distance).

Concept Used:

In the given figure, the bridge forms a right-angled triangle where:

The bridge acts as the hypotenuse.

The width of the river is the opposite side to the $$45^\circ$$​ angle.

​$$\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}}$$​​

Solution:

​​​​$$\sin 45^\circ = \frac{\text{Width of River}}{150}$$​​

​​​​$$\frac{1}{\sqrt{2}} = \frac{W}{150}$$​​

W = 150 $$\times \frac{1}{\sqrt{2}}$$​​

W= $$\frac{150}{\sqrt{2}}\times\frac{\sqrt{2}}{\sqrt{2}}$$​​

W=​$$75\sqrt{2}$$​​ m​

Option (B) is right.