1. 6.16.1 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

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

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

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

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

15. 6.26.2 The Law of Cosines

16. Quick Review

17. Quick Review Solutions

18. 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.

19. Law of Cosines

23. Example Solving a Triangle (SAS)

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

29. Chapter Test

31. 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 15 º is cut from the wheel, find the volume of the cheese wedge.

32. Chapter Test Solutions

34. 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 15 º is cut from the wheel, find the volume of the cheese wedge. ≈0.6 mi 405π/24≈53.01