# Geometry 8 5 The Tangent Ratio Trigonometry The

• Slides: 18

Geometry 8. 5 The Tangent Ratio

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

Tangent ratio = The tangent ratio is the ratio of the length of the legs in a Rt. ∆ Tangent of <A: opposite leg B Tangent of <B: adjacent leg hy pot enu se adjacent leg hy pot en use opposite leg A

I. Express tan X and tan Y as ratios. 1. 2. Z 9 X Y 3. 40 41 Y 21 4. Z X 29 4 Z 20 X Z 2 Y 8 X 8 Y

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

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

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.

5. tan 15 o = ______ 6. tan 43 o = ______ 7. tan 82 o = ______ 8. tan ____ =. 4663 9. tan _____ = 1. 5399 10. tan _____ = 2. 7475

Exercises. 2679 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 25˚ ≈. 4663 8. Complete: tan _____ Step 1. Locate. 4663 in the tangent column. Step 2. Go across to the angle column. Step 3. Read the value: 25˚

Answers to Exercises 6. . 9325 7. 7. 1154 9. 57˚ 10. 70˚

II. Find the value of x to the nearest tenth. 12. 11. 13. 17 25 x 14. x x 12 51 37 7. 4 x 72 3 15. 16. 17 17. A freeway ramp has a 10% grade. What angle does the ramp have with the ground? [Note: Grade(%) = y x 8 200 x 60 z

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

Exercises 13. Find the value of x to the nearest tenth. 17 x 7. 4

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

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

Answers to Exercises 12. 9. 2 14. 9. 7 16. x ≈ 115. 5, z ≈ 230. 9

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