AMC 12 2003b 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 $AC < 7$?

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