3.3.4 Practice - Modeling - The Pool Table Problem (Practice)

3.3.
4 Practice: Modeling: The Pool Table Practice

Problem
Geometry Honors Sem 1
Name:
Date:
Your Assignment: Bank Shot!
Setting Up for the Shot
You're playing a game of pool and it's your turn, but you have no direct shots. To
make any shot, you will need to bank the cue ball (the white 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 the side and then hits your
colored ball, moving it in the direction of a pocket (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 (side of pool table) 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 similar triangles to plan
your shot.
1. Which ball did you select? Red, yellow, or blue? (1 point: 1 point for selection)
2. Construct a triangle by performing each of these steps. (6 points: 1 point for each
step)
a. Label the cue (white) ball A.
3.3.4 Practice: Modeling: The Pool Table Problem 1/6

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b. Identify the pocket (hole) that you want your ball to go in. Label the center of this
pocket E.
(Hint: Click on the ball in the image on the Pool Table Problem page to see how to
make this shot.)
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 endpoint 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 of table) C is
on. Label the endpoint B.
f. Complete triangle ABC by drawing the line segment BC.

3. Complete 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. (2
points)
4. Assign a variable to name the length of BC and label it on your figure. To identify
the lengths of AB, CD, and DE, use the dimensions of the pool table. Some lengths
will include a variable. (4 points: 1 point for each label)
5. Use your similar triangles to set up a proportion. Solve this proportion for the
unknown variable, the length of BC. (5 points: 2 points for the proportion, 3 points for
the work)

6. To make your shot, you need 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 C 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. (2 points: 1 point for distance, 1 point
for location)
Peculiar Pool
It turns out that your pool table is a little weird. Usually, as you assumed in the
problem you solved above, the angle at which the ball bounces off the bumper is
equal to the angle at which it hits the bumper. But on this table, the ball bounces off
at the complement of that angle.
Now the cue ball is 13 inches from the top bumper. It is still 50 inches from the right
bumper. You need to figure out where to hit the cue ball so it rebounds off the top
bumper and strikes the other ball.

7. Sketch two triangles on the figure by following these steps. (3 points: 1 point for
each step)
a. 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 endpoint of the segment C.
b. Draw a line segment from C to A (the cue ball). Draw a perpendicular line
segment from A to the same bumper (side of table) C is on. Label the endpoint
B.
c. Complete ΔABC and ΔCED by drawing line segments BC and CD.
8. Let x represent the length of BC. Write expressions for the lengths of AB, CD, and
DE. (3 points: 1 point for each expression)

9. Explain why the triangles you drew are similar. Write a similarity statement for
these triangles. (2 points: 1 point for the explanation, 1 point for the statement)
10. Solve for x. Show your work. Then state (to the nearest tenth of an inch) how far
to the left of corner pocket D the cue ball must hit the upper bumper. (2 points: 1 point
for finding x, 1 point for location)
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3.3.

4 Practice: Modeling: The Pool Table Practice

Your Assignment: Bank Shot!

Setting Up for the Shot

a. Label the cue (white) ball A.

3.3.4 Practice: Modeling: The Pool Table Problem 1/6

f. Complete triangle ABC by drawing the line segment BC.

3.3.4 Practice: Modeling: The Pool Table Problem 2/6

3.3.4 Practice: Modeling: The Pool Table Problem 3/6

3.3.4 Practice: Modeling: The Pool Table Problem 4/6

c. Complete ΔABC and ΔCED by drawing line segments BC and CD.

3.3.4 Practice: Modeling: The Pool Table Problem 5/6

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3.3.4 Practice: Modeling: The Pool Table Problem 6/6

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