1. Warm Up(You need a Calculator!!!!!)
Write each fraction as a decimal rounded to the nearest hundredth.
Solve each equation.
0.67
0.29
x = 7.25
x = 7.99

2. 8-2
Trigonometric Ratios
Holt Geometry

3. A trigonometric ratio is a ratio of two sides of a right triangle.

5. SOH CAH TOA

6. Example 1A: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
sin J

7. Example 1C: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
tan K

8. Check It Out! Example 1a
Write the trigonometric ratio as a fraction and as a decimal rounded to
the nearest hundredth.
cos A

9. Example 2: Finding Trigonometric Ratios in Special Right Triangles
Use a special right triangle to write cos 30° as a fraction.
Draw and label a 30º-60º-90º ∆.

10. Use a special right triangle to write tan 45° as a fraction.
Check It Out! Example 2
Use a special right triangle to write tan 45° as a fraction. s
45°
Draw and label a 45º-45º-90º ∆.

11. Example 3A: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
sin 52°
Be sure your calculator is in degree mode, not radian mode.
Caution!
sin 52°  0.79

12. Example 3C: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
tan 65°
tan 65°  2.14

13. Check It Out! Example 3a
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
tan 11°
tan 11°  0.19

14. Find the length. Round to the nearest hundredth.BC
is adjacent to the given angle, B. You are given AC, which is opposite B. Since the adjacent and opposite legs are involved, use a tangent ratio.

15. Example 4A Continued
Write a trigonometric ratio.
Substitute the given values.
Multiply both sides by BC and divide by tan 15°.
BC  ft
Simplify the expression.

16. Example 4B: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth. QR
is opposite to the given angle, P. You are given PR, which is the hypotenuse. Since the opposite side and hypotenuse are involved, use a sine ratio.

17. Example 4B Continued
Write a trigonometric ratio.
Substitute the given values.
12.9(sin 63°) = QR
Multiply both sides by 12.9.
11.49 cm  QR
Simplify the expression.

19. 11.
12.

20. Lesson Quiz: Part I
Use a special right triangle to write each trigonometric ratio as a fraction.
1. sin 60° cos 45°
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
3. tan 84° 4. cos 13°
9.51
0.97

21. Lesson Quiz: Part II
Find each length. Round to the nearest tenth.
5. CB
6. AC
6.1
16.2
Use your answers from Items 5 and 6 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
7. sin A cos A tan A

22. Find each length. Round to the nearest tenth. 1. CB
Warm-Up
Find each length. Round to the nearest tenth.
1. CB
2. AC
6.1
16.2
Use your answers from Items 1 and 2 to write each trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
3. sin A cos A tan A 22