Question

In a circle of radius 5 miles, the length of the arc that subtends a central angle of 4 radians is how many miles?

Answer 1

The length of the arc is 20 miles.

Explanation:

We know that an arc formed by an angle of 1 radian in a circle of radius of 1 mile will have a length of 1 mile.

If the radius is 5 miles, an arc of 1 radian will have a length of 5 miles.

Then, if the angle is 4 radians, and the radius is 5 miles, we will have an arc length of:

`\text{arc length}=\text {angle} \cdot \text {radius}=4\cdot 5 =20\;\text{miles}`