How do you find arc length without knowing the radius?

You can use the degree measure of the central angle theta (the number of degrees you have gone around the circle) and the amount of radians you have gone around the circle

the equation for arc length using degrees and radians is: s (arc length) = r (xº)

r is not the radius length it is the length you have gone around the circle measured in terms of the radius

you need to know the central angle (degrees) and radians to figure out arc length without knowing the radius length