Question

There is a billiard table in the shape of a triangle whose angles are equal to \(90^{\circ}\), \(30^{\circ}\) and \(60^{\circ}\). 

Given a right triangle shaped billiard table, with "pockets" in its corners. One of its acute angles is \(30^{\circ}\). From this corner (the thirty-degree angle) a ball is launched towards the midpoint of the opposite side of the triangle (the median). Prove that if the ball is reflected more than eight times (angle of incidence equals angle of reflection), then eventually the ball will enter the "pocket" located at the 60-degree corner of the triangle.