Unit 10 Trigonometric Applications Review Problems Pre Calculus

Unit 10 – Trigonometric Applications Review Problems Pre. Calculus 10 -R

• Find the indicated side x. Please round the answer to the nearest tenth. 149. 3 Review Problems 1

• Find the indicated side x if b = 6, 3. 354 Review Problems 2

• Use the Law of Cosines to determine angle θ if a = 69. 19, b = 35. 97, c = 42. 82. 25. 97° 3

• Use the Law of Cosines to determine side x if a = 30, c = 36 and correct to two decimal places. 15. 44 4

• Solve triangle ABC, if a = 17, b = 10, and c = 23. 31, Review Problems 5

• Solve triangle ABC, if a = 71, Review Problems 6

• Find the indicated side x if b = 6, 3. 354 Review Problems 7

• 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 Review Problems 8

• 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

• 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

Find the indicated power ( 1 + i ) 16 256 Review Problems 11

Find the indicated power -1 Review Problems 12

Find the indicated power Review Problems 13

Find the square roots of: Review Problems 14

Find the fourth roots of: – 625 i Review Problems 15

Solve the following equation: Review Problems 16

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

For vectors u = <3, 4>, v = <– 1, 3>, find u + v = <2, 7> Review Problems 18

Given that u =<6, 3>, v =<– 2, 1>, find 7 u – 4 v 7 u – 4 v = <50, 17> Review Problems 19

u = <10, – 1>, v = <10, – 4>, find |u – v| = 3 Review Problems 20

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

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. 60 lb, Vertical: – 23. 87 lb Review Problems 22

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 Review Problems 23

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 Review Problems

Find: assuming u = 4 i + j, v = i – 7 j – 33 Review Problems 25

Find the component of u along v. u = < – 9, – 8 >, v = < 3, 2 > Review Problems 26

A constant force F = < 10, 3 > moves an object along a straight line from the point P(1, 2) to the point Q(8, 10). Find the work done if the distance is measured in feet and the force is measured in pounds. 94 ft-lb Review Problems 27

A lawn mower is pushed a distance of 120 ft along a horizontal path by a constant force of 20 lb. The handle of the lawn mower is held at an angle y = 60 from the horizontal. Find the work done. 1200. 00 ft-lb Review Problems 28

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. 3 i – 5 j Review Problems 29

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° Review Problems 30

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 Review Problems 31

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 Review Problems 32

Find the area of a triangle with sides of length 9 and 13 and included angle 56° 48. 499 Review Problems 33

Find the area of a triangle with sides of length 9, 20 and 13. 44. 900 Review Problems 34

Find side x if b = 9, c = 18, and 10. 785 Review Problems 35

Write the complex number in trigonometric form Review Problems 36

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True False Review Problems 50

False True Review Problems 51

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63 Review Problems

1. 2. 3. 4. 5. 149. 3 3. 354 25. 97° 15. 44 c = 23. 31, 11. 256 12. -1 13. 14. 15. 6. 7. 8. 9. 10. 3. 354 11. 4 miles 31. 15° 178. 44 ft 16. 17. 18. u + v = <2, 7> 19. 7 u – 4 v = <50, 17> 20. |u – v| = 3 Review Problems

21. 22. Horizontal: 25. 60 lb, Vertical: – 23. 87 lb 23. v = 763. 8 mi/h 24. a = 110° 25. – 33 26. 27. 94 ft-lb 28. 1200. 00 ft-lb 29. 3 i – 5 j 30. 53. 7° 31. No Solution 32. Two Solutions 33. 48. 499 34. 44. 900 35. 10. 785 36. 37. 38. 39. Review Problems

40. 47. 41. 42. 48. 43. 49. 44. 45. 46. 50. True, False Review Problems

51. False, True 52. 57. 58. 53. 59. 54. 60. 55. 61. 56. 62. Review Problems