1. 8-2 Trigonometric Ratios Warm Up Lesson Presentation Lesson Quiz
Holt Geometry

2. Write each fraction as a decimal rounded to the nearest hundredth.
Warm Up
Write each fraction as a decimal rounded to the nearest hundredth.
Solve each equation.
0.67
0.29
x = 7.25
x = 7.99

3. Objectives Find the tangent of an acute angle.
Use trigonometric ratios to find side lengths and angles in right triangles.

4. Vocabulary
trigonometric ratio
tangent

5. By the AA Similarity Postulate, a right triangle with a given acute angle is similar to every other right triangle with that same acute angle measure. So ∆ABC ~ ∆DEF ~ ∆XYZ, and These are trigonometric ratios. A trigonometric ratio is a ratio of two sides of a right triangle.

6. Note 66

7. In trigonometry, the letter of the vertex of the angle is often used to represent the measure of that angle. For example, the tangent of A is written as tan A.
Writing Math

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

9. Example 1B: Finding Trigonometric Ratios
Write the trigonometric ratio as a fraction and as a decimal rounded to the nearest hundredth.
Tan K

10. Example 2: Finding Trigonometric Ratios in Special Right Triangles
Use a special right triangle to write tan 30° as a fraction.

11. 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°

12. Example 3C: Calculating Trigonometric Ratios
Use your calculator to find the trigonometric ratio. Round to the nearest hundredth.
tan 65°
Be sure your calculator is in degree mode, not radian mode.
Caution!
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. Example 4A: Using Trigonometric Ratios to Find Lengths
Find the length. Round to the nearest hundredth. BC

15. Caution!
Do not round until the final step of your answer. Use the values of the trigonometric ratios provided by your calculator.

16. Example 4C: Using Trigonometric Ratios to Find Lengths
Find the length and the missing angle. Round to the nearest hundredth. ED D

17. Check It Out! Example 4c
Find the length and the missing angle. Round to the nearest hundredth. BC A

18. Exit Slip
Use a special right triangle to write each trigonometric ratio as a fraction.
1. tan 60° tan 45°
Use your calculator to find each trigonometric ratio. Round to the nearest hundredth.
3. tan 84°
Find each length. Round to the nearest tenth.
4. CB