10.1: The Tangent Ratio

1. 10.1: The Tangent Ratio • Expectation: • G1.3.1: Define the sine, cosine, and tangent of acuteangles in a right triangle as ratios of sides. Solve problems about angles, side lengths, or areas using trigonometric ratios in right triangles. 10.1: The Tangent Ratio

2. The length of arc XY of a circle is equal to ⅙ of the circumference of the circle. The length of the arc is 7π inches? What is the radius, in inches, of the circle? 10.1: The Tangent Ratio

3. Tangent • a. Draw Δ ABC w/ m A=40, m  B = 90 and AB=2 • b. Draw Δ DEF w/ m  D=40, m  E = 90 and DE=2.5 • c. Draw Δ GHI w/ m  G=40, m  H = 90 and GH=3 10.1: The Tangent Ratio

4. Tangent • d. Determine BC, EF and HI • e. Compare 10.1: The Tangent Ratio

5. Tangent Ratio • Defn: In a right triangle with acute angle,  A, with a measure of θ (theta), the tangent of A (tan A = tan A = tan θ) is the ratio of the length of the leg oppositeA to the length of the leg adjacent to A. 10.1: The Tangent Ratio

6. opposite Tan θ = adjacent opposite θ adjacent 10.1: The Tangent Ratio

7. opposite Tan α = adjacent α adjacent opposite 10.1: The Tangent Ratio

8. Give the tangent of A and B for the triangle below. A 13 5 B 12 10.1: The Tangent Ratio

9. Using a Trig Table (page 870) • What is tan θ if: • a. θ = 30 • b. θ = 75 10.1: The Tangent Ratio

11. Arc Tangent • The arc tangent tells us the measure of the angle with the given tangent ratio. 10.1: The Tangent Ratio

12. Arc Tangent • What is θ if: • a. tan θ = 1.483 • b. tan θ = .176 10.1: The Tangent Ratio

14. TAN tangent θ TAN-1 arc tangent θ Tangent on a Calculator Calculator must be set in degree mode!!!!!! 10.1: The Tangent Ratio

15. Using your calculator, what is: • tan 23? • tan 45? 10.1: The Tangent Ratio

16. What is the measure of an angle whose tangent ratio is: • .6532 • .0175 10.1: The Tangent Ratio

17. B 5 C A 12 Calculate the measure of A to the nearest tenth of a degree. 10.1: The Tangent Ratio

18. Calculate BC below to the nearest hundredth. B 34° A C 15 10.1: The Tangent Ratio

19. Calculate AC below to the nearest hundredth. B 10 18° A C 10.1: The Tangent Ratio

20. The directions for assembling a pool ladder state that the ladder should be placed at an angle of 75 relative to level ground. Which of the following expressions gives the distance in feet, that the ladder should be placed away from the bottom edge of the pool to comply with the directions? • A. • B. • C. • D. 6 tan 75 • E. tan (6 75°) 10.1: The Tangent Ratio

21. Ice Cream Anyone? • Ben and Jerry are on one side of river and Edy is on the other. • Ben is 20 meters directly south of Jerry. • Jerry and Edy are directly across the river from each other. 10.1: The Tangent Ratio

22. Ice Cream Anyone? • If Ben points at Edy and Jerry at the same time, his arms form a 54° angle. • How far is it across the river? Round your answer to the nearest tenth of a meter. 10.1: The Tangent Ratio

23. J E 20 54° B 10.1: The Tangent Ratio

24. B 5 1 A C • As shown in the figure below, what is the tangent of angle C? 10.1: The Tangent Ratio

25. Assignment • pages 635-637, • # 13-33 (odds), 35-39 (all) 10.1: The Tangent Ratio