how do you find the radius of a sector when the angle is 20 degrees and the arc length is 12cm?

$$b = \text{ arc length }= 12cm$$

$$\alpha = 20 \ensuremath{^\circ}$$

r = radius  ?

$$\boxed{b=2\pi r\frac{\alpha\ensuremath{^\circ}}{360\ensuremath{^\circ}}}$$

$$\\\\ \Rightarrow r = \dfrac{b*180\ensuremath{^\circ}}{\pi*\alpha\ensuremath{^\circ}} \\\\ r = \dfrac{12\;cm*180\ensuremath{^\circ}}{\pi*20\ensuremath{^\circ}}=34,377\;cm$$

The radius is 34.377 cm