3.3.4 Practice: Modeling: The Pool Table Problem-PLEASE HELP! 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.

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 Cis 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)