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

To find the width of the river, we can use trigonometry. Here's the detailed solution:

### Given:
1. The angle the bridge makes with the river bank is 45°.
2. The length of the bridge across the river is 150 m.

### Explanation:
The situation forms a right triangle where:
- The bridge is the hypotenuse (length = 150 m).
- The width of the river is the opposite side to the angle (let's denote it as `w`).
- The angle between the river bank and the bridge is 45°.

We use the sine function, which relates the opposite side (width of the river) to the hypotenuse in a right triangle:
\[ \sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}} \]

Substitute the known values:
\[ \sin(45^\circ) = \frac{w}{150} \]

The sine of 45° is a well-known trigonometric value:
\[ \sin(45^\circ) = \frac{\sqrt{2}}{2} \]

So:
\[ \frac{\sqrt{2}}{2} = \frac{w}{150} \]

Solve for `w`:
\[ w = 150 \times \frac{\sqrt{2}}{2} \]
\[ w = 75\sqrt{2} \]

Now approximate `w` by substituting the value of `\sqrt{2}` (approximately 1.414):
\[ w = 75 \times 1.414 \]
\[ w \approx 106.05 \]

### Final Answer:
The width of the river is approximately 106.05 m.