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Name ________________________________________ Date __________________ Class__________________ LESSON 13-1 Practice B Right-Angle Trigonometry Find the value of the sine, cosine, and tangent functions for θ. 1. 2. ________________________ 3. ________________________ ____________________ Use a trigonometric function to find the value of x. 4. 5. ________________________ 6. ________________________ ____________________ Find the values of the six trigonometric functions for θ. 7. 8. 9. _______________________________ _______________________________ ________________________ _______________________________ _______________________________ ________________________ Solve. 10. A water slide is 26 feet high. The angle between the slide and the water is 33.5°. What is the length of the slide? ___________________ 11. A surveyor stands 150 feet from the base of a viaduct and measures the angle of elevation to be 46.2°. His eye level is 6 feet above the ground. What is the height of the viaduct to the nearest foot? ___________________ 12. The pilot of a helicopter measures the angle of depression to a landing spot to be 18.8°. If the pilot’s altitude is 1640 meters, what is the horizontal distance to the landing spot to the nearest meter? ___________________ Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 13-4 Holt Algebra 2 c. S = a1 ; 40 ft 1− r 2. 30 ft 2. 3 4 3 , , 5 5 4 4. 12 5 12 , , 13 13 5 3. 60 8 40 6 30 3 15 1 5 b. cos 45° = c. cos 45° = x 12 2 2 2 d. x = 12 4. Let x = drop height and y = total vertical distance; y = 5x 5. A 9 40 9 , , 41 41 40 5.a. Cosine Drop Height (ft) Total Vertical Distance (ft) 12 3. 6. 10 7. 8 8. 9 9. 45 ft Practice B 6. J 1. 4 3 4 ; ; 5 5 3 2. 3. 12 5 12 ; ; 13 13 5 4. 6 3 5. 44 3 3 6. 7 Reading Strategy 1. Possible answer: A diverging series increases as the number of terms increases. There is no limit to the sum. The graph looks similar to the exponential function. 7. sin θ = 2. No; a converging series approaches a constant number but never reaches it. 12 5 12 ; cos θ = ; tan θ = 13 13 5 13 13 5 ; sec θ = ; cot θ = 12 5 12 csc θ = 3. a. Converging b. Diverging c. Diverging 8. sin θ = 3 4 3 ; cos θ = ; tan θ = 5 5 4 csc θ = 5 5 4 ; sec θ = ; cot θ = 3 4 3 d. Converging 4. Diverging; possible answer: because there would be no limit to the total payout, the amount I receive would increase each year. 9. sin θ = 9 40 9 ; cos θ = ; tan θ = 41 41 40 csc θ = 41 41 40 ; sec θ = ; cot θ = 9 40 9 LESSON 13-1 10. 47 ft Practice A 9 40 9 ; ; 41 41 40 11. 162 ft 12. 4817 m 48 24 1. a. sinθ = = 50 25 Practice C b. cosθ = 14 7 = 50 25 1. 7 24 7 ; ; 25 25 24 2. c. tanθ = 48 24 = 14 7 3. 60 11 60 ; ; 61 61 11 4. 20 3 5. 3.4 3 4 3 4 ; ; 5 5 3 6. 16 Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A52 Holt Algebra 2