



 
Hi, Suppose the length of the arc is $a$ units, the radius of the circle is $r$ units and the angle measurement is $t$ degrees as in the diagram. The circumference of the circle is $2 \pi \; r$ units and $a$ the length of the arc is a fraction of the circumference. The angle measurement all the way around the circle is 360 degrees and the angle measurement $t$ is a fraction of this. By the symmetry of the circle these two fractions are equal. That is \[\frac{a}{2 \pi \; r} = \frac{t}{360}.\] Solving this for $a$ gives the more familiar expression \[a = 2 \pi \; r \frac{t}{360}.\] Since you know $a$ and $t$ you can solve for $r.$ If you measure the angle $t$ in radians rather than degrees the expression is simpler. If the angle is measured in radians the expression is \[ a = r t.\] I hope this helps,  


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