1. PreCalculus 6-R Additional Topics in Trigonometry Unit 6 Review Problems

2. Review Problems Find the indicated side x. Please round the answer to the nearest tenth. 149.3 1

3. Review Problems Find the indicated side x if b = 6, 3.354 2

4. Use the Law of Cosines to determine angle θ if a = 69.19, b = 35.97, c = 42.82. 25.97° 3

5. Use the Law of Cosines to determine side x if a = 30, c = 36 and correct to two decimal places. 15.44 4

6. Review Problems Solve triangle ABC, if a = 17, b = 10, and c = 23.31, 5

7. Review Problems Solve triangle ABC, if a = 71, 6

8. Review Problems Find the indicated side x if b = 6, 3.354 7

9. Review Problems Two straight roads diverge at an angle of 30 degrees. Two cars leave the intersection at 5:00 P.M., one traveling at 45 mi/h, and the other at 35 mi/h. How far apart are the cars at 5:30 P.M. 11.4 miles 8

10. Two tugboats that are 118 ft apart pull a barge, as shown. If the length of one cable is 206 and the length of the other is 227, find the angle formed by the two cables. 31.15° 9

11. A 50 foot tower is located on the side of a mountain that is inclined 35° to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 145 feet downhill from the base of the tower. Find the shortest length of wire needed. 178.44 ft 10

12. Review Problems A river flows due south at 5 mi/h. A swimmer attempting to cross the river heads due east swimming at 3 mi/h relative to the water. Find the true velocity of the swimmer as a vector. 3i –5j 11

13. Review Problems Sketch the triangle and then solve the triangle (if possible) for angle A. If two solutions exist, find both. Please round the answer to the nearest tenth. 53.7° 12

14. Review Problems Sketch the triangle and then solve the triangle (if possible). If two solutions exist, find both. Please round the answer to the nearest tenth. No Solution 13

15. Review Problems Sketch the triangle and then solve the triangle (if possible). If two solutions exist, find both. Please round the answer to the nearest tenth. Two Solutions 14

16. Review Problems Find the area of a triangle with sides of length 9 and 13 and included angle 56° 48.499 15

17. Review Problems Find the area of a triangle with sides of length 9, 20 and 13. 44.900 16

18. Review Problems Find the vector with initial point P (6, 8) and terminal point Q (4, 4). 17

19. Review Problems For vectors u =, v =, find u + v u + v = 18

20. Review Problems Given that u =, v =, find 7 u – 4 v 7u – 4v = 19

21. Review Problems u =, v =, find |u – v|. |u – v| = 3 20

22. Review Problems Find the horizontal and vertical components of the vector v, where |v| = 34,. Write the vector in the form 21

23. Review Problems A man pushes a lawn mower with a force of 35 lb exerted at an angle of 43 to the ground. Find the horizontal and vertical components of the force. Horizontal: 25.60lb, Vertical: –23.87lb 22

24. Review Problems A jet is flying through a wind that is blowing with a speed of 56 mi/h in the direction N 40 E. The jet has a speed of 708 mi/h in still air, and the pilot heads the jet in the direction N 35 E. Find the true speed of the jet. v = 763.8 mi/h 23

25. Review Problems A straight river flows east at a speed of 7 mi/h. A boater starts at the south shore of the river and heads in a direction a from the shore (see the figure). The motorboat has a speed of 20 mi/h in still water. The boater wants to arrive at a point on the north shore of the river directly opposite the starting point. In what direction should the boat be headed? a = 110 ° 24

26. Review Problems True False 25

27. Review Problems False True 26

28. Review Problems 27

29. Review Problems 28

30. Review Problems Find side x if b = 9, c = 18, and 10.785 29

31. Review Problems 30

32. Review Problems 31

33. Review Problems 32

34. Review Problems 33

35. Review Problems 34

36. Review Problems 35

37. Review Problems 36

38. Review Problems 37

39. Review Problems 38

40. Review Problems 39

41. Review Problems 40

42. Review Problems 41

43. Review Problems 1.149.3 2.3.354 3.25.97° 4. 15.44 5.c = 23.31, 6. 7. 3.354 8. 11.4 miles 9. 31.15° 10. 178.44 ft 11. 3i –5j 12. 53.7° 13. No Solution 14. Two Solutions 15. 48.499 16. 44.900 17. 18. u + v = 19. 7u – 4v = 20. |u – v| = 3

44. Review Problems 21. 22.Horizontal: 25.60lb, Vertical: –23.87lb 23. v = 763.8 mi/h 24. a = 110 ° 25. True, False 26. False, True 27. 28. 29. 10.785 30. 31. 32. 33. 34. 35. 36. 37. 38.

45. Review Problems 39. 40. 41.