You’re playing a game of pool and it’s your turn but you have no direct shots. To make any shots you will need to bank the cue ball off the side of the table before it hits your ball.
That means that you hit the cue ball so that it bounces off of the side and then hits your colored ball moving in the direction of a hole. The angle that the ball hits the bumper is equal to the angle that it bounces off the bumper.
The cue ball is 18 inches from the top bumper and 50 inches from the right bumper. The dimensions of the pool table are 96 inches in the horizontal direction by 46 inches in the vertical direction.
Use the illustration of the table and what you know about some of the triangles to plan your shot.
1( Already chosen). Which ball did you select red yellow or blue?
I selected the red ball
2 Part 1. Construct a triangle by performing each of these steps
A. label the cue(white) ball A.
B. Identify the pocket (hole) that you want your ball to go in label the center of his pocket E.
C. draw a line segment that starts at E, goes through the colored ball, and ends at the other side of the table. Label the other end point of the segment C.
D. draw a line segment from C to
A(the cue ball). This segment will make the same angle with the bumper as CE.
E. Draw a perpendicular line segment from a to the same bumper(side if the table) C is on. Label the endpont B.
F. Complete the triangle ABC by drawing the line segment BC.
2 Part 2.
A. Complete the triangle CDE that is similar to ABC. Where does D need to be to create a similar triangle? Label vertex D and mark the angles that have the same measure.
B. assign a variable to name the length of BC and label it on your figure. To identify the length of a B, CD & DE, use the dimensions of the pool table. Some lengths will include a variable.
C. Use your similar triangles to set up a proportion. Solve this proportion from the unknown variable, the length of BC.
D. To make your shot, you need to use the cue ball to hit point C. Find length CD and use it to identify the location of C in relation to one of the corner pockets. For example if she is on the upper bumper your answer might be : 15 inches to the right of the upper left pocket. Round your answer to the nearest inch.
