Chapter 7 - Pearson

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$College of Marin Study Guide for Math 95 A,B - Pearson Learning ...$

112 Chapter 7 Applications of Trigonometry and Vectors24.2680 m25. 58.6 feet26. 11 feet long27. 13 meters tall28. 15.8 ft apart29. 53.2 ft30. C » 77.131. 115 km32. 2.4 miles33. 25 sq units34. The sides of the triangle measure 5, 10, and5 5 , which satisfy the converse of thePythagorean theorem: the area is 25 sq units35. a – b36. a + 3c37. 207 lb38. 209 newtons39. horizontal: 869; vertical: 41840. horizontal: 25 2; vertical: 25 241. magnitude: 15Angle: 126.9(θ lies in quadrant II)42. magnitude: 29Angle: 316.4(θ lies in quadrant IV)43. (a) i(b) 4i-2j(c) 11i-7j44. -9;142.145. The vectors are orthogonal.46. θ = 4547. 29 lb48. The force is 280 newtons (rounded) at an angleof 30.4° with the first boat.49. The pilot should fly on a bearing of 306°. Heractual speed is 524 mph.50. 4º51. 34 lb52. The resulting speed is 21 km per hr (rounded)and bearing is 118°53. Newton’s formula:Therefore,54. Mollweide’s formula:Therefore,a+ b cos ( A-B)=c sin C2+ 3 2+3=2 22- 3 2-3=2 21 2 1 2a- b cos ( A-B)=c cos C12 1 2Copyright © 2013 Pearson Education, Inc.
Chapter 7 Test 11355. Let a = 2, b = 2 3 , A = 30°, B = 60°.Verifytan 12( A- B)a-b= .tan 1 ( A B)a + b2 +tan 1( A-B) tan 1(30-60 )2 2=tan 1( A+ B) tan 1(30+ 60 )2 2tan( -15 )= »-0.26794919tan 45a-b2-2 3 2-2 3 4- 8 3+12= ⋅ =a+ b 2+ 2 3 2-2 3 4-1216-8 3= =- 2 + 3 »-0.26794919-8Thus,tan 12( A- B)a-b=tan 1 ( A B)a + b2values of a, b, A, and B.Chapter 7 Test1. 137.5°2. 179 km.3. 49.0°4. 168 sq units+using the given11. (a) 1, – 3(b) - 6, 18(c) - 20(d) 1012. 41.813. Since the dot product is 0, the vectors areorthogonal.14. The balloon is 2.7 miles off the ground.15. - 346, 45116. 1.91 miles17. 14 m18. 30 lb19. The plane’s bearing is 357°20. 18.75. 18 sq units6. (a) b > 10(b) none(c) b ≤ 107. a » 40 m; B » 41 ;C = 798. B1 » 58 30 ¢ or B2= 12130¢Solving separately for triangles A 1 = 8300¢a 11250 in. ; A 2 = 2000 ¢ ; a 2 » 431 in.9. magnitude: v = 10;angle: 126.9(θ lies in quadrant II)10.Copyright © 2013 Pearson Education, Inc.
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Chapter 7 - Pearson

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