1. Geometry 8.5 The Tangent Ratio

2. Trigonometry The word trigonometry comes from the Greek words that mean “triangle measurement.” In this course we will introduce the trigonometry of right triangles.

3. Tangent ratio = opposite leg adjacent leg hypotenuse opposite leg adjacent leg A B Tangent of <A: Tangent of <B: The tangent ratio is the ratio of the length of the legs in a Rt. ∆

4. X Y Z 940 41 X Y Z 29 20 21 X Y Z 2 4 X Y Z 88 I. Express tan X and tan Y as ratios. 1.2.3.4.

5. Exercises: tan = 9 41 40 Y 1. Express tan X and tan Y as ratios. X Z

6. Exercises: tan = 2 4 2√3 Y 3. Express tan X and tan Y as ratios. XZ

7. Answers to Exercises 2. 4.

8. Table of Trigonometric Ratios Turn to page 311 in your textbook. This table gives approximate decimal values of the tangent ratio for some angles. The table also can be used to find an angle measure when given a tangent value.

9. 5. tan 15 o = ______6. tan 43 o = ______7. tan 82 o = ______ 8. tan ____ =.46639. tan _____ = 1.539910. tan _____ = 2.7475

10. Exercises 5. Complete: tan 15˚ ≈ _____ Step 1. Locate 15˚ in the angle column. Step 2. Go across to the tangent column. Step 3. Read the value:.2679.2679 8. Complete: tan _____ ≈.4663 Step 1. Locate.4663 in the tangent column. Step 2. Go across to the angle column. Step 3. Read the value: 25˚ 25˚

11. Answers to Exercises 6..9325 7. 7.1154 9. 57˚ 10. 70˚

12. x 25 37  3 72  x x12 51  7.4 x 17  x 17 yy 8 60  200 x z 11. 17. A freeway ramp has a 10% grade. What angle does the ramp have with the ground? [Note: Grade(%) = II. Find the value of x to the nearest tenth. 12.13.14. 15. 16.

13. Exercises 11. Find the value of x to the nearest tenth. x 25 37˚

14. Exercises 13. Find the value of x to the nearest tenth. 7.4 x 17 

15. Exercises 15. Find the value of x and y to the nearest tenth. x 17 yy 8

16. Exercises 17. A freeway ramp has a 10% grade. What angle does the ramp have with the ground? 1 10 ramp ground

17. Answers to Exercises 12. 9.2 14.9.7 16. x ≈ 115.5, z ≈ 230.9

18. Homework pg. 308 #1-24 Add hypotenuse, the three proportions, Pythag and Converse, multiply fractions vs. proportions, 45-45-90 and 30-60-90 formulas, pythagorean triples to vocab list, tangent