1. Copyright © 2011 Pearson, Inc. 5.6 Law of Cosines

2. Copyright © 2011 Pearson, Inc. Slide 5.6 - 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. Copyright © 2011 Pearson, Inc. Slide 5.6 - 3 Law of Cosines

4. Copyright © 2011 Pearson, Inc. Slide 5.6 - 4 Example Solving a Triangle (SAS)

5. Copyright © 2011 Pearson, Inc. Slide 5.6 - 5 Example Solving a Triangle (SAS)

6. Copyright © 2011 Pearson, Inc. Slide 5.6 - 6 Example Solving a Triangle (SAS)

7. Copyright © 2011 Pearson, Inc. Slide 5.6 - 7 Area of a Triangle

8. Copyright © 2011 Pearson, Inc. Slide 5.6 - 8 Heron’s Formula

9. Copyright © 2011 Pearson, Inc. Slide 5.6 - 9 Example Using Heron’s Formula Find the area of a triangle with sides 10, 12, 14.

10. Copyright © 2011 Pearson, Inc. Slide 5.6 - 10 Example Using Heron’s Formula Find the area of a triangle with sides 10, 12, 14.

11. Copyright © 2011 Pearson, Inc. Slide 5.6 - 11 Quick Review

12. Copyright © 2011 Pearson, Inc. Slide 5.6 - 12 Quick Review

13. Copyright © 2011 Pearson, Inc. Slide 5.6 - 13 Quick Review

14. Copyright © 2011 Pearson, Inc. Slide 5.6 - 14 Chapter Test

15. Copyright © 2011 Pearson, Inc. Slide 5.6 - 15 Chapter Test

16. Copyright © 2011 Pearson, Inc. Slide 5.6 - 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. Copyright © 2011 Pearson, Inc. Slide 5.6 - 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 15 º is cut from the wheel, find the volume of the cheese wedge.

18. Copyright © 2011 Pearson, Inc. Slide 5.6 - 18 Chapter Test Solutions

19. Copyright © 2011 Pearson, Inc. Slide 5.6 - 19 Chapter Test Solutions

20. Copyright © 2011 Pearson, Inc. Slide 5.6 - 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. Copyright © 2011 Pearson, Inc. Slide 5.6 - 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 15 º is cut from the wheel, find the volume of the cheese wedge. 405π/24 ≈ 53.01