Draw a diagram of the pool table, labeling the dimensions of the table and the position of the cue ball.
Since the cue ball is 18 inches from the top bumper and 50 inches from the right bumper, you can draw a right triangle with these side lengths.
The dimensions of the pool table can also be used to draw a right triangle, with the horizontal dimension (96 inches) as the base and the vertical dimension (46 inches) as the height.
These two triangles are similar because they are both right triangles and they share a right angle. Therefore, the ratios of their sides are equal.
You can use the ratios of the sides of these triangles to determine the angle at which you should aim your shot. To do this, you can set up a proportion using the corresponding sides of the two triangles. For example, you could use the ratio of the base to the height of the small triangle (18 inches to 50 inches) and set it equal to the ratio of the base to the height of the large triangle (96 inches to 46 inches). Solving this proportion will give you the value of the angle you need to aim your shot.
I hope this helps you solve the problem! If you have any questions ask.