Work out radius from arc sector and angle

Question

I am trying to work out the radius of a sector with arc length of 47.6 and a angle of 210. I tried a formula which was $r=\frac{L}{2π}\times \frac{360}{\theta}$ I saw but kept ending up with 128.176

Thank you for reading.

Answer 1

In a circle, $l = r\theta$ where $\theta$ is in radians.

Therefore, $r = {l\over \theta}$ where $\theta = {7\pi\over 6}$ and $l=47.6$. This gives $r = 12.98$