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Homework, Page 484

Homework, Page 484. Solve the triangle. 1. Homework, Page 484. Solve the triangle. 5. Homework, Page 484. Solve the triangle. 9. Homework, Page 484. State whether the given measurements determine zero, one, or two triangles. 13. Homework, Page 484.

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Homework, Page 484

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  1. Homework, Page 484 Solve the triangle. 1.

  2. Homework, Page 484 Solve the triangle. 5.

  3. Homework, Page 484 Solve the triangle. 9.

  4. Homework, Page 484 State whether the given measurements determine zero, one, or two triangles. 13.

  5. Homework, Page 484 State whether the given measurements determine zero, one, or two triangles. 17.

  6. Homework, Page 484 Two triangles can be formed using the given measurements. Find both triangles. 21.

  7. Homework, Page 484 Decide whether the triangle can be solved using the Law of Sines. If so, solve it, if not, explain why not. 25. Neither triangle can be solved using the Law of Sines, for the one on the left we need to know the length of the side opposite the known angle and for the one on the right, we have the same problem.

  8. Homework, Page 484 Respond in one of the following ways: (a) State: “Cannot be solved with Law of Sines.” (b) State: “No triangle is formed.” (c) solve the triangle. 29. No triangle is formed. The largest side of a triangle is opposite the largest angle and angle A must be the largest angle and side a is no the largest side.

  9. Homework, Page 484 Respond in one of the following ways: (a) State: “Cannot be solved with Law of Sines.” (b) State: “No triangle is formed.” (c) solve the triangle. 33.

  10. Homework, Page 484 37. Two markers A and B on the same side of a canyon rim are 56 ft apart. A third marker C, located on the opposite rim, is positioned so that (a) Find the distance between C and A. (b) Find the distance between the canyon rims.

  11. Homework, Page 484 41. A 4-ft airfoil attached to the cab of a truck makes an 18º angle with the roof and angle β is 10º. Find the length of the vertical brace positioned as shown.

  12. Homework, Page 484 45. Two lighthouses A and B are known to be exactly 20 mi apart. A ship’s captain at S measures the angle S at 33º. A radio operator measures the angle B at 52º. Find the distance from the ship to each lighthouse.

  13. Homework, Page 484 49. The length x in the triangle is (A) 8.6 (B) 15.0 (C) 18.1 (D) 19.2 (E) 22.6

  14. Homework, Page 484 53. (a) Show that there are infinitely many triangles with AAA given if the sum of the three positive angles is 180º. Consider the triangle formed with its base on a radius that is one-half the diameter of a semi-circle. If the opposite ends of the radius are connected to a point on the semi-circle, a triangle is formed. Since there are an infinite number of possible values of the radius, there must be an infinite number of possible triangles.

  15. Homework, Page 484 53. (b) Give three examples of triangles where A = 30º, B = 60º, and C = 90º. (c) Give three examples where A = B = C = 60º.

  16. Homework, Page 484 57. Towers A and B are known to be 4.1 mi apart on level ground. A pilot measures the angles of depression to the towers at 36.5º and 25º, respectively. Find distances AC and BC and the height of the aircraft.

  17. 5.6 The Law of Cosines

  18. Quick Review

  19. Quick Review Solutions

  20. What you’ll learn about • Deriving the Law of Cosines • Solving Triangles (SAS, SSS) • Triangle Area and Heron’s Formula • Applications … and why The Law of Cosines is an important extension of the Pythagorean theorem, with many applications.

  21. Deriving theLaw of Cosines

  22. Law of Cosines

  23. Example Solving a Triangle (SAS)

  24. Example Solving a Triangle (SSS)

  25. Area of a Triangle

  26. Heron’s Formula

  27. Example Using Heron’s Formula Find the area of a triangle with sides 10, 12, 14.

  28. Example Finding the Area of a Regular Circumscribed Polygon Find the area of a regular nonagon (9-sided) circumscribed about a circle of radius 10 in.

  29. Example Surveyor’s Problem Tony must find the distance from point A to point B on opposite sides of a lake. He finds point C which is 860 ft from point A and 175 ft from point B. If he measures the angle at point C between points A and B as 78º, what is the distance between points A and B.

  30. Homework • Homework Assignment #1 • Review Section 5.6 • Page 494, Exercises: 1 – 53 (EOO)

  31. What you’ll learn about • Two-Dimensional Vectors • Vector Operations • Unit Vectors • Direction Angles • Applications of Vectors … and why These topics are important in many real-world applications, such as calculating the effect of the wind on an airplane’s path.

  32. Directed Line Segment

  33. Two-Dimensional Vector

  34. Two-Dimensional Vector

  35. Initial Point, Terminal Point, Equivalent

  36. Magnitude

  37. Example Finding Magnitude of a Vector

  38. Vector Addition and Scalar Multiplication

  39. Example Performing Vector Operations

  40. Unit Vectors

  41. Example Finding a Unit Vector

  42. Standard Unit Vectors

  43. Resolving the Vector

  44. Example Finding the Components of a Vector

  45. Example Finding the Direction Angle of a Vector

  46. Velocity and Speed The velocity of a moving object is a vector because velocity has both magnitude and direction. The magnitude of velocity is speed.

  47. Example Writing Velocity as a Vector

  48. Example Calculating the Effects of Wind Velocity

  49. Example Finding the Direction and Magnitude of the Resultant Force

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