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For what values of theta will the ball strike? [ILL 1974]

Source:

January 2, 2011
trigonometry

Problem Statement

Let a,ba, b, and cc denote the three sides of a billiard table in the shape of an equilateral triangle. A ball is placed at the midpoint of side aa and then propelled toward side bb with direction defined by the angle θ\theta. For what values of θ\theta will the ball strike the sides b,c,ab, c, a in that order?
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