Question

How do I find the arc length with given radius & central angel?

Answer 1

The length of an arc subtended by a central angle is proportional to the circle's circumference. If the given central angle has measure
`\theta` and the circle has radius
`r`, then the arc has length
`\ell` such that

`\frac{\ell}\theta=(2\pi r)/(2\pi)=r`

where
`\theta` is given in radians. Then

`\ell=r\theta`

If
`\theta` is given in degrees, then

`\frac{\ell}\theta=(2\pi r)/(360)\implies\ell=(\theta\pi r)/(180)`