Question

What is the arc length of the subtending arc for an angle of 72 degrees on a circle of radius 4?

Answer 1

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:


`(2\pi r)/(2\pi)=(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
`\frac{180^\circ}{\pi\text{ rad}}`.


`L=4*\left(72^\circ*\frac{\pi\text{ rad}}{180^\circ}\right)=4*\frac{2\pi}5=\frac{8\pi}5\approx5.0265`