a boy travels in a boat at an angle of 20 degrees to the river bank.if he travels 200m before reaching the opposite bank,calculate the width of the river

sin 20 = w/200

w = 200 sin 20

68.40402867

To calculate the width of the river, we can use trigonometry. Let's break down the information given:

1. The boy travels in a boat at an angle of 20 degrees to the river bank.
2. He travels 200m before reaching the opposite bank.

To find the width of the river, we need to focus on the information given in the problem. Let's draw a diagram to make it easier to understand:

```
|
| /
| /
| / x (unknown width of the river)
| /
| /
- - -|-------------- y (200m)
| /
|/
```

In the diagram above, we have a right-angled triangle. The base of the triangle represents the width of the river (x), the height of the triangle represents the distance the boy has traveled (200m), and the angle between the base and the hypotenuse is 20 degrees.

To find the width of the river (x), we can use the trigonometric function tangent (tan):

tan(angle) = opposite/adjacent

In this case, the opposite side is 200m (y) and the adjacent side is the width of the river (x).

So, we have:

tan(20 degrees) = y/x

We can rearrange the equation to solve for x:

x = y / tan(20 degrees)

Plugging in the values:

x = 200m / tan(20 degrees)

After evaluating the expression using a calculator, you should find that the width of the river (x) is approximately 572.96 meters (rounded to two decimal places).