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Geometry

This course introduces the concept of trigonometry, focusing specifically on the tangent ratio of right triangles. The tangent ratio, defined as the ratio of the length of the opposite leg to the adjacent leg, plays a crucial role in understanding triangle measurement. Students will learn how to calculate tangent values and relate them to angles, with practical exercises to reinforce their understanding. The course will utilize a trigonometric ratio table for estimating decimal values and finding angle measures from given tangent values.

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Geometry

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

  4. Z Y Z Z X 9 40 8 8 2 4 Y X 29 21 41 X Y X Y Z 20

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

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

  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 15o = ______ 6. tan 43o = ______ 7. tan 82o = ______ 8. tan ____= .4663 9. tan _____= 1.5399 10. tan _____= 2.7475

  10. 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˚ 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˚

  11. Answers to Exercises • .9325 • 7.1154 • 57˚ • 70˚

  12. x 25 x 17 x 12 37 x 51 7.4 72 3 17 y x 8 200 60 x z 11. 17. A freeway ramp has a 10% grade. What angle does the ramp have with the ground? [Note: Grade(%) =

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

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

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

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

  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

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