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5.6

5.6. Law of Cosines. 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. Law of Cosines.

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5.6

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  1. 5.6 Law of Cosines

  2. 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.

  3. Law of Cosines

  4. Example Solving a Triangle (SAS)

  5. Example Solving a Triangle (SAS)

  6. Example Solving a Triangle (SAS)

  7. Area of a Triangle

  8. Heron’s Formula

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

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

  11. Quick Review

  12. Quick Review

  13. Quick Review

  14. Chapter Test

  15. Chapter Test

  16. Chapter Test 9. A hot-air balloon is seen over Tucson, Arizona, simultaneously by two observers at points A and B that are 1.75 mi apart on level ground and in line with the balloon. The angles of elevation are as shown here. How high above ground is the balloon?

  17. Chapter Test 10. A wheel of cheese in the shape of a right circular cylinder is 18 cm in diameter and 5 cm thick. If a wedge of cheese with a central angle of 15º is cut from the wheel, find the volume of the cheese wedge.

  18. Chapter Test Solutions

  19. Chapter Test Solutions

  20. Chapter Test Solutions 9. A hot-air balloon is seen over Tucson, Arizona, simultaneously by two observers at points A and B that are 1.75 mi apart on level ground and in line with the balloon. The angles of elevation are as shown here. How high above ground is the balloon? ≈ 0.6 mi

  21. Chapter Test Solutions 10. A wheel of cheese in the shape of a right circular cylinder is 18 cm in diameter and 5 cm thick. If a wedge of cheese with a central angle of 15º is cut from the wheel, find the volume of the cheese wedge. 405π/24 ≈ 53.01

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