Question

A central angle 0, in a circle of radius 4 ft intercepts an arc length of 50 ft.

Calculate the radian measure of 0.

Answer 1

Given:

The central angle =
`\theta`

Radius of the circle = 4 ft

Intercepted arc length = 50ft

To find:

The value of
`\theta` in radian measure.

Solution:

The formula for arc length is

`s=r\theta`

where, r is radius and
`\theta` is the central angle in radians.

Putting s=50 and r=4, we get

`50=4\theta`

Divide both sides by 4.

`(50)/(4)=\theta`

`12.5=\theta`

Therefore, the value of
`\theta` is 12.5 radians.