Name: Period Score /27 Version: A Math 11 - Adult Education - Trigonometry Short Answer Show any work and the answer in the space provided. 1. (1 point) What is the reference angle for 215 in standard position? 2. (1 point) What are the three other angles in standard position that have a reference angle of 88? 3. (1 point) Determine the exact value for sin330. 4. (2 points) A salvage vessel locates a sunken ship directly below it. The angle of depression from the salvage vessel to one end of the ship is 27.5 and to the other end is 41.9. If the length of the ship to be salvaged is known to be 171 m, determine how far beneath the water s surface it is, to the nearest metre. 1
5. (1 point) Determine, to the nearest tenth of a degree, the two possible measures of C. 6. (2 points) Two trawlers left harbour at the same time. One sails at 14 km/h on a bearing of 321 and the other at 18 km/h on a bearing of 343. To the nearest tenth of a kilometre, how far apart are the two trawlers after 3 hours. 7. (1 point) Determine the measure of x, to the nearest tenth of a degree. 2
8. (2 points) Determine, to the nearest tenth of a centimetre, the two possible lengths of a. 9. (1 point) If B = 53.6, c = 8.9 cm, and b = 10.1 cm, and ABC is acute, what is the measure of C, to the nearest tenth of a degree? 3
10. (1 point) The point ( 19, 4) is on the terminal arm of A. Determine the set of exact primary trigonometric ratios for A? 11. (2 points) An airplane is flying over a town, between two tracking stations. The angle of elevation from Station 1 is 38 and from Station 2 is 29. If the stations are 2300 m apart, what is the altitude of the plane, to the nearest tenth of a metre? 12. (1 point) What is the length of x, to the nearest tenth of a metre? 4
13. (1 point) While flying, a helicopter pilot spots a water tower that is 5.1 km to the north. At the same time, he sees a monument that is 7.9 km to the south. The tower and the monument are separated by a distance of 11.8 km along the flat ground. What is the angle made by the water tower, helicopter, and monument? 14. (1 point) Determine the length of x, to the nearest tenth of a centimetre. 15. (1 point) Given that tan A = 19 and that A is located in the third quadrant, determine exact values for the 18 other two primary trigonometric ratios. 5
16. (1 point) If Q = 36, r = 11 cm, and p = 17 cm, what is the length of q, to the nearest centimetre? 17. (1 point) Determine the exact value for tan315. 18. (2 points) Solve FVM, if v = 11.2 cm, m = 39.5 cm, and V = 15. Provide answers to the nearest degree and the nearest tenth of a centimetre. 19. (2 points) The angle of elevation between Emma and a kite is 23. When she walks 40 metres closer to the kite the angle of elevation increases to 36. To the nearest metre, how high above the ground is the kite? 6
20. (2 points) A clock has two hands that are 11 cm and 14 cm long. What is the distance, to the nearest tenth of a centimetre, between the tips of the hands at 2 p.m.? 7
Math 11 - Adult Education - Trigonometry Answer Section SHORT ANSWER 1. 35 2. 92, 268, 272 3. 1 2 4. The angle made by the salvage ship and the two ends of the sunken vessel is 180 27.5 41.9 = 110.6. Solution 1 sin110.6 171 = sin41.9 side length side length = 122 sin27.5 = depth 122 depth = 56.3 metres 5. 158.1 and 1.9 6. The trawlers would be 21.8 kilometres apart. 7. 29.0 8. 68.2 cm and 25.3 cm 9. 45.2 10. sin A = 4 19, cos A = 377 377, tan A = 4 19 Solution 2 sin110.6 171 sin41.9 = depth 84.35 = sin27.5 side length 11. The angle made by the plane and the two tracking stations is 180 38 29 = 113. side length = 84.35 depth = 56.3 metres Solution 1 Solution 2 sin113 2300 = sin29 d d = 1211.36 sin113 2300 = sin38 d d = 1538.31 sin38 = a 1211.36 a = 745.8 metres sin29 = a 1538.31 a = 745.8 metres 1
12. 16.3 m 13. 129 14. 2.9 15. Since tana = y,then y = 19 and x = 18 in the third quadrant. x So, x 2 + y 2 = r 2 18 2 + 19 2 = r 2 324 + 361 = r 2 685 = r 2 685 = r Since the angle is in the third quadrant, sina = 19 685 16. 10 cm 17. 1 sinv 18. = sinm v m sin15 11.2 = sinm 39.5 sinm = 39.5 sin15 11.2 and cosa = 18 685. sinm 0.9128 M sin 1 (0.9128) 66 or 114 F = 180 (15 + 66 ) = 99 F = 180 (15 + 114 ) = 51 sinv = sinf sin15 v f 11.2 = sin99 f f = 42.7 sinv v = sinf f sin15 11.2 = sin51 f f = 51 FVM has V = 15, M = 66, F = 99, v=11.2, m=39.5, f=42.7 or V = 15, M = 114, F = 51, v=11.2, m=39.5, f=33.6 2
19. Solution 1 tan 23 = tan 36 = h x h x + 40 x + 40tan 23 = x tan 36 x + 40tan 23 = h x tan 36 = h 40tan 23 = x tan 36 xtan 23 40tan 23 = xtan 36 tan 23 40tan 23 tan 36 tan 23 = x 56.2 metres = x tan 36 = h 56.2 h = 56.2tan 36 = 41 metres Solution 2 144 is supplementary to 36 13 completes the obtuse triangle sin 23 hypotenuse hypotenuse = sin36 = h 69.5 69.5sin36 = h 41 = h = sin 13 40 40sin 23 sin 13 = 69.5 20. At 2 p.m., the hour hand is 2 of the distance around the clock. 12 2 360 = 60 12 The angle formed by the two hands measures 60. Let x represent the distance between the tips of the hands. x 2 = 14 2 + 11 2 21411 cos 60 x 12.8 The distance between the tips of the hands at 2 p.m. is approximately 12.8 cm. 3