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

$\dfrac{\ell}\theta=\dfrac{2\pi r}{2\pi}=r$

where $\theta$ is given in radians. Then

$\ell=r\theta$

If $\theta$ is given in degrees, then

$\dfrac{\ell}\theta=\dfrac{2\pi r}{360}\implies\ell=\dfrac{\theta\pi r}{180}$