Question

What is the radius of a circle in which a 30° arc is 2 pi inches long

Answer 1

\[arclength = r \theta\]when the angle is measured in radians, so if we convert 30° to radians we get\[2 \pi = r * 30° * (2 \pi radians/360°) = r * (\pi/6) radians\]
\[r = 2 \pi/(\pi/6) = 12 inches\]