A billiard ball is struck by a cue. It travels
100

cm
100cm100, start text, c, m, end text before ricocheting off a rail and traveling another
120

cm
120cm120, start text, c, m, end text into a corner pocket. The angle between the path as the ball approaches the rail and the path after it strikes the rail is
4
5
∘
45
∘
45, degrees.
How far is the corner pocket from where the cue initially struck the ball?
Do not round during your calculations. Round your final answer to the nearest centimeter.