Directions (or bearings) on Earth are measured in degrees, running from zero to $360^\circ$, clockwise, starting with $0^\circ$ being due North. So due East for example, is $90^\circ$, due South $180^\circ$, and Northwest is $315^\circ$.
You are swinging a rock clockwise (looking from above) around your head and you are trying to hit a broom stick $12$ feet due east of you. The rock moves in a circle of a radius of $3$ feet around your head. When you release your sling the rock will continue to move along the tangent to the circle though its position at the time of the release.
When you release the rock the sling is pointing in a direction of degrees.
Ignore the vertical motion of the rock.

It's unrealistic, but remember that unless otherwise stated WeBWorK expects your answer to be within one tenth of one percent of the true answer.

Hint: You can solve this problem using calculus and computing the tangent to a circle. However, you can also solve it using plain trigonometry. The moral is that you want to use whatever requires the least amount of fuss for the problem at hand.