Let \(L\) be the length of an arc subtended by an angle of \(\theta\) on a circle of radius \(r\). Then the ratio of the arc's length to its subtended angle is proportional with the circle's entire circumference to one complete revolution:
\(\dfrac{2\pi r}{2\pi}=\dfrac{L}{\theta}\)
Solving for \(L\) yields the formula for arc length of a circular arc,
\(L=r\theta\)
where \(\theta\) is in radians. To convert to degrees, use the conversion factor \(\dfrac{180^\circ}{\pi\text{ rad}}\).
\(L=4\times\left(72^\circ\times\dfrac{\pi\text{ rad}}{180^\circ}\right)=4\times\dfrac{2\pi}5=\dfrac{8\pi}5\approx5.0265\)
