9.3: Ratios of Right Triangles
This activity is intended to supplement Geometry, Chapter 8, Lesson 5.
Problem 1 – Exploring Right Triangle Trigonometry
We will begin this activity by looking at the definitions of the sine, cosine, and tangent of a right triangle. Start the Learning Check application by pressing APPS and selecting LearnChk. Open the file Right Triangle Trigonometry. You are given the definition for the sine, cosine, and tangent of a right triangle. Copy the definitions onto your worksheet.
1. What is the definition of
2. What is the definition of
3. What is the definition of
Answer the following questions about sine, cosine, and tangent for
4. What is
5. What is
6. What is
7. What is
8. What is
9. What is
Problem 2 – Exploring the Sine Ratio of a Right Triangle
For this problem, we will investigate the sine ratio. Start the Cabri Jr. application by pressing
10. Grab and drag point
Position 





1  
2  
3  
4 
11. What do you notice about the ratio of
12. Did
Because the ratio remains the same and
13. What is the measurement of
14. What is the measurement of
Problem 3 – Exploring the Cosine Ratio of a Right Triangle
For this problem, we will investigate the sine ratio. Start the Cabri Jr. application and open the file TRIG. You are given right triangle
15. Collect data for four positions of point
Position 





1  
2  
3  
4 
Because the ratio remains the same, and
16. What is the measurement of \begin{align*}\angle{A}\end{align*}?
17. What is the measurement of \begin{align*}\angle{B}\end{align*}?
18. How would you solve an equation of the form \begin{align*}\tan A = \frac{BC}{AC}\end{align*}?
Problem 4 – Applying the Sine, Cosine, and Tangent Ratio of a Right Triangle
Find and label the measure of each angle given two sides of the right triangle.
19.
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26.