1. trigonometry trigonometric ratio sine cosine tangent Find trigonometric ratios using right triangles. Solve problems using trigonometric ratios.

2. G.1 The student understands the structure of, and relationships within, an axiomatic system. (B) Recognize the historical development of geometric systems and know mathematics is developed for a variety of purposes. G.11 The student applies the concepts of similarity to justify properties of figures and solve problems. (C) Develop, apply, and justify triangle similarity relationships, such as right triangle ratios, trigonometric ratios, and Pythagorean triples using a variety of methods.

4. Find Sine, Cosine, and Tangent Ratios Find sin L, cos L, tan L, sin N, cos N, and tan N. Express each ratio as a fraction and as a decimal.

5. Find Sine, Cosine, and Tangent Ratios

8. Answer:

9. A.A B.B C.C D.D Lesson 4 CYP1 A. Find sin A. A. B. C. D.

10. A.A B.B C.C D.D Lesson 4 CYP1 B. Find cos A. A. B. C. D.

11. A.A B.B C.C D.D Lesson 4 CYP1 C. Find tan A. A. B. C. D.

12. A.A B.B C.C D.D Lesson 4 CYP1 D. Find sin B. A. B. C. D.

13. A.A B.B C.C D.D Lesson 4 CYP1 E. Find cos B. A. B. C. D.

14. A.A B.B C.C D.D Lesson 4 CYP1 F. Find tan B. A. B. C. D.

15. Use a Calculator to Evaluate Expressions A. Use a calculator to find tan 56° to the nearest ten thousandth. Answer: tan 56° ≈ 1.4826 KEYSTROKES: 56 1.482560969 ENTERTAN

16. Use a Calculator to Evaluate Expressions B. Use a calculator to find cos 89° to the nearest ten-thousandth. Answer: cos 89° ≈ 0.0715 KEYSTROKES: 89 0.071452406 ENTERCOS

17. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.0.669 B.1.111 C.0.743 D.0.731 A. Use a calculator to find sin 48° to the nearest thousandth.

18. Lesson 4 CYP2 1.A 2.B 3.C 4.D A.0.0872 B.0.9962 C.11.4301 D.0.0698 B. Use a calculator to find cos 85° to the nearest ten thousandth.

19. Use Trigonometric Ratios to Find a Length EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches.

20. Use Trigonometric Ratios to Find a Length Answer: The treadmill is about 7.3 inches high. Multiply each side by 60. Use a calculator to find y. KEYSTROKES: 60 7 7.312160604 ENTERSIN

21. 1.A 2.B 3.C 4.D Lesson 4 CYP3 A.1 in. B.11 in. C.16 in. D.15 in. CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the nearest inch?

22. COORDINATE GEOMETRY Find m  X in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1). Use Trigonometric Ratios to Find an Angle Measure

23. PlanUse the Distance Formula to find the measure of each side. Then use one of the trigonometric ratios to write an equation. Use the inverse to find Explore You know the coordinates of the vertices of a right triangle and that is the right angle. You need to find the measures of one of the angles. Solve or

24. Use Trigonometric Ratios to Find an Angle Measure or

25. Use Trigonometric Ratios to Find an Angle Measure Use the cosine ratio. Simplify. Solve for x.

26. Use Trigonometric Ratios to Find an Angle Measure Use a calculator to find Examine Use the sine ratio to check the answer. Simplify. KEYSTROKES: 4 5 ENTER 2ND ÷)

27. Answer: The measure of  X is about 36.9. Use Trigonometric Ratios to Find an Angle Measure KEYSTROKES: 3 5 ENTER 2ND ÷)

28. A.A B.B C.C D.D Lesson 4 CYP4 A.66.0° B.56.3° C.33.7° D.24.0° COORDINATE GEOMETRY Find m  A in right ΔABC to the nearest degree.