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6.1

6.1. The Law of Sines. Quick Review. Quick Review Solutions. What you’ll learn about. Deriving the Law of Sines Solving Triangles (AAS, ASA) The Ambiguous Case (SSA) Applications … and why The Law of Sines is a powerful extension of the triangle congruence theorems of Euclidean geometry.

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6.1

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  1. 6.1 The Law of Sines

  2. Quick Review

  3. Quick Review Solutions

  4. What you’ll learn about • Deriving the Law of Sines • Solving Triangles (AAS, ASA) • The Ambiguous Case (SSA) • Applications … and why The Law of Sines is a powerful extension of the triangle congruence theorems of Euclidean geometry.

  5. Law of Sines

  6. Example Solving a Triangle Given Two Angles and a Side

  7. Example Solving a Triangle Given Two Angles and a Side

  8. Example Solving a Triangle Given Two Sides and an Angle (The Ambiguous Case)

  9. Example Solving a Triangle Given Two Sides and an Angle (The Ambiguous Case)

  10. A 65º x B 15ft 15º C Example Finding the Height of a Pole

  11. A 65º x B 15ft 15º C Example Finding the Height of a Pole

  12. 6.2 The Law of Cosines

  13. Quick Review

  14. Quick Review Solutions

  15. 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.

  16. Law of Cosines

  17. Example Solving a Triangle (SAS)

  18. Example Solving a Triangle (SAS)

  19. Area of a Triangle

  20. Heron’s Formula

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

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

  23. Chapter Test

  24. Chapter Test

  25. 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? 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.

  26. Chapter Test Solutions

  27. Chapter Test Solutions

  28. 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 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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