The length of an arc subtended by a central angle is proportional to the circle's circumference. If the given central angle has measure [tex]\theta[/tex] and the circle has radius [tex]r[/tex], then the arc has length [tex]\ell[/tex] such that
[tex]\dfrac{\ell}\theta=\dfrac{2\pi r}{2\pi}=r[/tex]
where [tex]\theta[/tex] is given in radians. Then
[tex]\ell=r\theta[/tex]
If [tex]\theta[/tex] is given in degrees, then
[tex]\dfrac{\ell}\theta=\dfrac{2\pi r}{360}\implies\ell=\dfrac{\theta\pi r}{180}[/tex]
