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Problem

Lukas is playing pool on a table shaped like an equilateral triangle. The pockets are at the corners of the triangle and are labeled $C$, $H$, and $T$. Each side of the table is $16$ feet long. Lukas shoots a ball from corner $C$ of the table in such a way that, on the second bounce, the ball hits $2$ feet away from him along side $CH$.

(a) How many times will the ball bounce before hitting the pocket?

(b) Which pocket will the ball hit?

(c) How far will the ball travel before hitting the pocket?

Attempt

I tried graphing it using the coordinate system but it would be very challenging even if I did find where it first hits a pocket (the line) how many bounces occurred.

Official solution

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Questions

I am having a hard time seeing where $\dfrac{7}{8}n$ and $\dfrac{15}{8}n$ are coming from. Can someone provide a diagram and explain that?

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