9.3: Ratios of Right Triangles
This activity is intended to supplement Geometry, Chapter 8, Lesson 5.
ID: 11576
Time Required: 45 minutes
Activity Overview
In this activity, students will explore the ratios of right triangles. Students will discover that they can find the measure of the angles of a right triangle given the length of any two sides.
Topic: Right Triangles & Trigonometric Ratios
 Sine
 Cosine
 Tangent
Teacher Preparation and Notes
 This activity was written to be explored on the TI84 with the Cabri Jr. and Learning Check applications.
 Before beginning this activity, make sure that all students have the Cabri Jr. applications. Also, make sure students have or know the trigonometric definitions.
 To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
 To download the calculator file, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=11576 and select TRIG.
Associated Materials
 Student Worksheet: Ratios of Right Triangles http://www.ck12.org/flexr/chapter/9693, scroll down to the third activity.
 Cabri Jr. Application
 TRIG.8xv
Problem 1 – Exploring Right Triangle Trigonometry
You may need to allow students to use a textbook (or other resource) to find the definitions of sine, cosine, and tangent.
Students are asked to give the ratio of several triangles on their handheld or their accompanying worksheet.
Problem 2 – Exploring the Sine Ratio of a Right Triangle
For this problem, students will investigate the sine ratio of two sides of a triangle. Students should start the Cabri Jr. app and open the file Trig.8xv.
Students will collect data on their worksheets by moving point
Students will discover that the ratio of
Students will need to answer several questions on their handhelds or their accompanying worksheets.
Problem 3 – Exploring the Cosine Ratio of a Right Triangle
Students will repeat the exploration in Problem 2, but with the cosine ratio.
Problem 4 – Applying the Sine, Cosine, and Tangent Ratio of a Right Triangle
In Problem 4, students are asked to apply what they have learned about how to find the measure of an angle of a right triangle given two sides of the triangle.
Solutions
1. For right triangle
2. For right triangle
3. For right triangle
4.
5.
6.
7.
8.
9.
10. Sample answers:
Position 





1  2.4376781463393  6.2006451991814  0.39313298342907  23.149583787224 
2  3.0769811671077  7.8268201774092  0.39313298342907  23.149583787224 
3  3.6665092204124  9.3263841370716  0.39313298342906  23.149583787223 
4  4.3154341679767  10.977034107736  0.39313298342905  23.149583787222 
11. The ratio does not change.
12. No, the angle does not change.
13. 23.1496
14. 66.8504
15. Sample answers:
Position 





1  7.0816099136391  8.8549125969341  0.7997379800328  36.894911430193 
2  8.0238624186986  10.033114118664  0.79973798003277  36.894911430196 
3  9.0235078139592  11.283080257848  0.79973798003279  36.894911430194 
4  3.7704816328074  4.7146462053143  0.79973798003281  36.894911430192 
16. 36.8949
17. 53.1051
18.
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20.
21.
22.
23.
24.
25.
26.
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