Ch6prac 1.Find the degree measure of the angle with the given radian measure. (Round your answer to the nearest whole number.) -2 2. Find the degree measure of the angle with the given radian measure. 3. Find the radian measure of the angle with the given degree measure. (Round your answer to three decimal places.) 5760 4. The measure of an angle in standard position is given. Find two positive angles and two negative angles between -720 and 1080 that are coterminal with the given angle. 5. The measures of two angles in standard position are given. Determine whether the angles are coterminal.-20, 340 6. Find an angle between 0 and 360 that is coterminal with the given angle. 376 7. Find an angle between 0 and 2π that is coterminal with the given angle. Give your answer in terms of π. 8. A circular arc of length 13 ft subtends a central angle of 25. Find the radius of the circle. Round your answer to 3 decimal places. 8. Find the radius of each circle if the area of the sector is 32. (Round your answer to two decimal places.) 9. A sector of a circle of radius 23 mi has an area of 388 mi 2. Find the central angle of the sector. Round your answer to 2 decimal places. 10. How many revolutions will a car wheel of diameter 30 inches make as the car travels a distance of eight miles? (Round your answer to the nearest whole number.) 11. Find (a) sin(α) and cos(β), (b) tan(α) and cot(β), and (c) sec(α) and csc(β). Assume x = 2, y = 5. 12. Find the side labeled x. Round your answer to 5 decimal places. Assume a = 22, θ = 51. 13. Sketch a triangle that has acute angle θ, and find the other five trigonometric ratios of θ. 14. Solve the right triangle. Assume h = 411. (a) Find the length of the shorter side. (Round your answer to two decimal places.) (b) Find the length of the longer side. (Round your answer to two decimal places.) (c) Find the other angle.
15. Find x correct to one decimal place. Assume A = 81. 16. From the top of a 165 ft lighthouse, the angle of depression to a ship in the ocean is 23. How far is the ship from the base of the lighthouse? Round your answer to the nearest foot. 17. A 16-ft ladder is leaning against a building. If the base of the ladder is 7 ft from the base of the building, what is the angle of elevation of the ladder? (Round your answer to one decimal place.) How high does the ladder reach on the building? (Round your answer to the nearest whole number.) 18. To measure the height of the cloud cover at an airport, a worker shines a spotlight upward at an angle 75 from the horizontal. An observer at a distance D = 505 m away measures the angle of elevation to the spot of light to be 45. Find the height h of the cloud cover, correct to the nearest meter. 19. Write the first trigonometric function in terms of the second for θ in the given quadrant. cot θ, sin θ; θ in quadrant II 20. Find the values of the trigonometric functions of θ from the information given. cos(θ) = -4/17, and θ in quadrant III 21. Find the values of the trigonometric functions of θ from the information given. cot θ = 1/6, sin θ < 0 22. Find the area of a triangle that has the following dimensions. Round your answer to the tenth place. sides of length 4 and 3, and included angle 82. 23. Find the area of the shaded region in the figure where α = π/3, b = 13. (Round your answer correct to the nearest whole number). 24. Use the Law of Sines to find the indicated angle θ. Assume C = 64, b = 56.6, c = 80.9. (Round your answer to one decimal place.) 25. Use the Law of Sines to find the indicated side x. Assume A = 109, B = 26, a = 170. (Round your answer to one decimal place.)
26. Solve the triangle using the Law of Sines. Assume b = 4, A = 40, C = 120. (Round the lengths to the 27. nearest hundredth and the angle to the nearest whole number.) Use the following information to sketch the triangle, and then solve the triangle using the Law of Sines. (Round the angle to the nearest whole number and the lengths to the nearest tenth.) A = 35, B = 115, c = 48 28a Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (Below, enter your answers so that smaller than C 2. Round your answers to the nearest degree and to the nearest tenth of length.) a = 30, c = 46, A = 30 C 1 is 28b Use the Law of Sines to solve all possible triangles that satisfy the given conditions if possible. a 50, b 100, A 135 28c Use the Law of Sines to solve all possible triangles that satisfy the given conditions if possible. a 26, c 15, C 29 29. For the triangle shown, find the length AD. Assume u = 19, v = 19, x = 25, y = 25. (Round your answer to two decimal places.) 30. A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, 15 mi apart, to be 32 and 48, as shown in the figure. Round your answers to the nearest tenth mile. (a) Find the distance of the plane from point A. (b) Find the elevation of the plane. 31. Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that CAB = 48.9. He also measures CA as 316 ft and CB as 527 ft. Find the distance between A and B. Round your answer to the nearest foot. (Note: ABC is an acute angle.) 32. A tree on a hillside casts a shadow c ft down the hill. If the angle of inclination of the hillside is b to the horizontal and the angle of elevation of the sun is a, find the height of the tree. Assume a = 53, b = 23 c = 245 ft. (Round your answer to the nearest whole number 33. A water tower 30 m tall is located at the top of a hill. From a distance of D = 160 m down the hill, it is observed that the angle formed between the top and base of the tower is 8. Find the angle of inclination of the hill. Round your answer to the nearest tenth degree.
34. Use the Law of Cosines to determine the indicated side x. θ = 89 35. Use the Law of Cosines to determine the angle θ. x = 125.6 36. Use the Law of Cosines to determine the angle θ. (Round your answer to one decimal place.) a = 18, b = 11, c = 37. Solve triangle ABC. (If there is no such triangle enter NONE for each answer. Round your answers to 1 decimal place.) b = 50, c = 25, A = 69 38. Solve triangle ABC. (If there is no such triangle enter NONE for each answer.) a = 69, c = 51, C = 55 39. Find the angle θ. (Use either the Law of Sines or the Law of Cosines, as appropriate.) (Round your answer to one decimal place.) a = 14, b = 5, c = 15 40. Find the angle θ. (Use either the Law of Sines or the Law of Cosines, as appropriate.) (Round your answer to one decimal place.) a = 14, c = 8, C = 30 41. Find the area of the triangle whose sides have the given lengths. (Round your answer to two decimal places.) a = 5, b = 6, c = 6 42. Find the area of the shaded figure. (Round your answer to two decimal places.) a = 7, b = 10, y = 50 43. A parallelogram ABCD has lengths of sides and angles given below. Find the length of the diagonals AC and BD. (Round your answers to two decimal places.)
AB = DC = 9 and AD = BC = 7, A = 50 44. A car travels along a straight road, heading east for 1 h, then traveling for 30 min on another road that leads northeast. If the car has maintained a constant speed of 60 mi/h, how far is it from its starting position? Round your answer to 2 decimal places. 45. Airport B is 300 mi from airport A at a bearing N 50 E (see the figure). A pilot wishing to fly from A to B mistakenly flies due east at 250 mi/h for 40 minutes, when he notices his error. (a) How far is the pilot from his destination at the time he notices the error? Round your answer to the nearest mile. (b) What bearing should he head his plane in order to arrive at airport B? Round your answer to the nearest degree. 46. A 140 ft tower is located on the side of a mountain that is inclined 32 to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 55 ft downhill from the base of the tower. Find the shortest length of wire needed.