1. Splash Screen

2. Five-Minute Check (over Lesson 8–3) CCSS Then/Now New Vocabulary
Key Concept: Trigonometric Ratios
Example 1: Find Sine, Cosine, and Tangent Ratios
Example 2: Use Special Right Triangles to Find Trigonometric Ratios
Example 3: Real-World Example: Estimate Measures Using Trigonometry
Key Concept: Inverse Trigonometric Ratios
Example 4: Find Angle Measures Using Inverse Trigonometric Ratios
Example 5: Solve a Right Triangle
Lesson Menu

3. Find x and y. A. B. C. D.
5-Minute Check 1

4. Find x and y.
A. x = 5, y = 5
B. x = 5, y = 45 C. D.
5-Minute Check 2

5. The length of the diagonal of a square is centimeters
The length of the diagonal of a square is centimeters. Find the perimeter of the square.
A. 15 cm
B. 30 cm
C. 45 cm
D. 60 cm
5-Minute Check 3

6. The side of an equilateral triangle measures 21 inches
The side of an equilateral triangle measures 21 inches. Find the length of an altitude of the triangle.
A in.
B. 12 in.
C. 14 in.
D in.
5-Minute Check 4

7. ΔMNP is a 45°-45°-90° triangle with right angle P
ΔMNP is a 45°-45°-90° triangle with right angle P. Find the coordinates of M in Quadrant II for P(2, 3) and N(2, 8).
A. (–1, 3)
B. (–3, 3)
C. (5, 3)
D. (6, 2)
5-Minute Check 5

8. The hypotenuse of a 30°-60°-90° triangle measures inches
The hypotenuse of a 30°-60°-90° triangle measures inches. What is the length of the side opposite the 30° angle?
A. 10 in.
B. 20 in. C. D.
5-Minute Check 6

9. Mathematical Practices
Content Standards
G.SRT.6 Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
G.SRT.7 Explain and use the relationship between the sine and cosine of complementary angles.
Mathematical Practices
1 Make sense of problems and persevere in solving them.
5 Use appropriate tools strategically.
CCSS

10. Find trigonometric ratios using right triangles.
You used the Pythagorean Theorem to find missing lengths in right triangles.
Find trigonometric ratios using right triangles.
Use trigonometric ratios to find angle measures in right triangles.
Then/Now

11. trigonometry trigonometric ratio sine cosine tangent inverse sine
inverse cosine
inverse tangent
Vocabulary

12. The Trigonometric Functions
SINE
COSINE
TANGENT

13. The Trigonometric Functions
SINE
COSINE
TANGENT

14. Represents an unknown angle
Greek Letter q
Pronounced “theta”
Represents an unknown angle

15. Concept

16. Concept

17. Concept

18. Concept

19. Concept

20. Hey man just remember
Soh * Cah * Toa

21. Find Sine, Cosine, and Tangent Ratios
A. Express sin L as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

22. Find Sine, Cosine, and Tangent Ratios
B. Express cos L as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

23. Find Sine, Cosine, and Tangent Ratios
C. Express tan L as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

24. Find Sine, Cosine, and Tangent Ratios
D. Express sin N as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

25. Find Sine, Cosine, and Tangent Ratios
E. Express cos N as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

26. Find Sine, Cosine, and Tangent Ratios
F. Express tan N as a fraction and as a decimal to the nearest hundredth.
Answer:
Example 1

27. A. Find sin A. A. B. C. D.
Example 1

28. B. Find cos A. A. B. C. D.
Example 1

29. C. Find tan A. A. B. C. D.
Example 1

30. D. Find sin B. A. B. C. D.
Example 1

31. E. Find cos B. A. B. C. D.
Example 1

32. F. Find tan B. A. B. C. D.
Example 1

33. The side adjacent to the 60° angle has a measure of x.
Use Special Right Triangles to Find Trigonometric Ratios
Use a special right triangle to express the cosine of 60° as a fraction and as a decimal to the nearest hundredth.
Draw and label the side lengths of a 30°-60°-90° right triangle, with x as the length of the shorter leg and 2x as the length of the hypotenuse.
The side adjacent to the 60° angle has a measure of x.
Example 2

34. Use a calculator to find y.
Estimate Measures Using Trigonometry
Multiply each side by 60.
Use a calculator to find y.
KEYSTROKES:
ENTER
SIN
Answer: The treadmill is about 7.3 inches high.
Example 3

35. Definition of cosine ratio
Use Special Right Triangles to Find Trigonometric Ratios
Definition of cosine ratio
Substitution
Simplify.
Example 2

36. Use a special right triangle to express the tangent of 60° as a fraction and as a decimal to the nearest hundredth. A. B. C. D.
Example 2

37. 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°, about how high does the ramp rise off the ground to the nearest inch?
A. 1 in.
B. 11 in.
C. 16 in.
D. 15 in.
Example 3

38. STOP

39. Concept

40. Concept

41. Concept

42. Use a calculator to find the measure of P to the nearest tenth.
Find Angle Measures Using Inverse Trigonometric Ratios
Use a calculator to find the measure of P to the nearest tenth.
Answer: So, the measure of P is approximately 46.8°.
Example 4

43. Answer: So, the measure of P is approximately 46.8°.
Find Angle Measures Using Inverse Trigonometric Ratios
The measures given are those of the leg adjacent to P and the hypotenuse, so write the equation using the cosine ratio.
KEYSTROKES: [COS]
2nd ( ÷ )
ENTER
Answer: So, the measure of P is approximately 46.8°.
Example 4

44. Solve a Right Triangle
Solve the right triangle. Round side measures to the nearest hundredth and angle measures to the nearest degree.
Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06
Example 5

45. So, the measure of AB is about 8.06.
Solve a Right Triangle
So, the measure of AB is about 8.06.
Answer: mA ≈ 30, mB ≈ 60, AB ≈ 8.06
Example 5

46. Use a calculator to find the measure of D to the nearest tenth.
B. 48.3°
C. 55.4°
D. 57.2°
Example 4

47. Solve the right triangle
Solve the right triangle. Round side measures to the nearest tenth and angle measures to the nearest degree.
A. mA = 36°, mB = 54°, AB = 13.6
B. mA = 54°, mB = 36°, AB = 13.6
C. mA = 36°, mB = 54°, AB = 16.3
D. mA = 54°, mB = 36°, AB = 16.3
Example 5

48. End of the Lesson