Jeanette is playing in a 9-ball pool tournament. She will win if she sinks the 9-ball from the final rack, so she needs to line up her shot precisely. Both the cue ball and the 9-ball have mass m, and the cue ball is hit at an initial speed of v_i. Jeanette carefully hits the cue ball into the 9-ball off center, so that when the balls collide, they move away from each other at the same angle ? from the direction in which the cue ball was originally traveling (see figure). Furthermore, after the collision, the cue ball moves away at speed v_f, while the 9-ball moves at speed v₉. (Figure 1)

For the purposes of this problem, assume that the collision is perfectly elastic, neglect friction, and ignore the spinning of the balls.

Find the angle ? that the 9-ball travels away from the horizontal, as shown in the figure. Express your answer in degrees to three significant figures.