2003 AMC 12B Problem 21

An object moves 8 cm in a straight line from A to B, turns at an angle \alpha, measured in radians and chosen at random from the interval (0,\pi), and moves 5 cm in a straight line to C. What is the probability that AC < 7?

\mathrm{(A)}\ \frac{1}{6} \qquad\mathrm{(B)}\ \frac{1}{5} \qquad\mathrm{(C)}\ \frac{1}{4} \qquad\mathrm{(D)}\ \frac{1}{3} \qquad\mathrm{(E)}\ \frac{1}{2}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.