## Act 1

1. How far did the car travel on the final ramp?

2. Write down a guess.

## Act 2

3. What information would be useful to figure this out?

4. Write down some questions you have in your head right now.

Give students the opportunity to gather data with this GeoGebra applet. Encourage students to gather as much data as they need in order to determine a pattern for how far the car travels as the angle increases.

After students have explored the applet, they’ll need to determine the angle of elevation for the final ramp. Display the following image. If you’re using this lesson in an Algebra 1 class, consider giving students the angle measure since they haven’t learned Trigonometry yet.

The GeoGebra applet does not allow students to explore the actual angle measure of the final ramp, so they will need to use the pattern they discovered earlier to determine the distance the car travels on the final ramp.

## Act 3

## Sequel

5. Write an expression to represent the relationship between the angle of elevation and distance traveled.

6. How far would the car travel if the final ramp had a 40° angle of elevation?

**Common Core Standards**

HSF.BF.A.1

Write a function that describes a relationship between two quantities.

HSG.SRT.C.8

Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

**TEKS**

write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems

G.9(A)

determine the lengths of sides and measures of angles in a right triangle by applying the trigonometric ratios sine, cosine, and tangent to solve problems

**Credit: **Vintage car vector created by freepik – www.freepik.com