Question

How do you find the radius of a circle given the length of an arc?

Answer 1

The circle with radius `r` has a circumference `2*pi*r` which corresponds to an angle of `360^o`.

If you are given an arc of a certain angle lets say `p^o` degrees which is `l` in length then

`p^o/360^o=l/(2*pi*r)=>r=(360^o*l)/(2*pi*p^o)`

Answer 2

`r = (180 xxl)/( pi theta)`

Explanation:

You always need another piece of information, just the arc length is not enough - the circle could be big or small and the arc length does not indicate this.

It will help to be given the sector angle.

If you have the sector angle `theta`, and the arc length, `l` then you can find the radius

`r = (180 xxl)/(pi theta)`