# Lesson 16

Bank Shot

• Let’s use similarity to solve problems.

### 16.1: Notice and Wonder: Right Triangles

What do you notice? What do you wonder?

### 16.2: Bank Shot

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1. You need to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the solid orange 5 ball into the upper right corner pocket.
2. A true bank shot will create two similar right triangles. Determine the measures of the triangles you drew. Are they similar?
3. Calculate the exact point on the bottom side to aim for and then precisely draw the path of the ball.

How would you hit the ball so that it will end in the hole after one stroke?

### 16.3: Indirect Measurement (Mirrors)

Use mirrors to measure the height of a tall object. Label this image with the measurements you made.

Calculate the unknown height.

### 16.4: Indirect Measurement (No Mirrors)

What if you don’t have a mirror when you’re trying to measure the height of something too tall to measure directly? Brainstorm as many methods other than the mirror method as you can.

Where on the wall should we aim if we're standing at point $$A$$ and want the ball to land at point $$D$$? We know the triangles are similar because of the Angle-Angle Triangle Similarity Theorem. Segment $$AB$$ corresponds to segment $$DC$$. So the scale factor to go from triangle $$DCE$$ to triangle $$ABE$$ is $$\frac{16}{32}$$. Segments $$BE$$ and $$CE$$ also correspond so they must have the same scale factor. Since $$\frac{16}{32}=\frac{1}{2}$$, segments $$BE$$ and $$CE$$ must be in a $$1:2$$ ratio. Dividing the 20 foot wall into 3 equal parts tells us that $$BE = 6\frac{2}{3}$$. In practice it's easier to think about aiming for a third of the way along the wall from the right hand side than it is to aim for a spot $$6\frac{2}{3}$$ feet away from point $$B$$.