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