1. Chapter 6 Investigating Non-Right Triangles as Models for Problems: 6.6 Adjusting the Pythagorean Theorem: The Cosine Law

2. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Goal for Today: Learn about and apply the cosine law

3. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law *The same pattern holds true for any triangle for example, triangle XYZ *The same pattern holds true for any triangle for example, triangle XYZ *The same holds true for any triangle Ex. XYZ

4. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law The cosine law is used to find the 3 rd side of a triangle when 2 sides and a contained angle are known, or To find an angle when the length of 3 sides are known

5. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law 2 sides and a contained angle… ex. 1 A CB 7cm 5cm 43⁰ ?

6. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law

7. A CB 7cm 5cm 43 ⁰ ?

8. Humour Break

9. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law 3 sides and finding an angle… ex. 2 A CB 7cm 5cm 4.8 ?

10. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law 3 sides and finding an angle… ex. 2 ?

11. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law A CB 7cm 5cm 4.8

12. Homework Tuesday, January10th - Hwk 6.6 Cosine Law Hwk p.566, #2-10, 12a, 13ac

13. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 1 A bicycle race follows a triangular course. The three legs of the race are, in order, 2.3km, 5.9km, and 6.2km. Find the angle between the starting leg and the finishing leg to the nearest degree.

14. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 1 ? R 6.2km Q P 5.9km 2.3km

15. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 1

16. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law

17. Humour Break

18. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 2 The radar screen of an airport control tower shows that two plans are at the same altitude. According to the range finder, one plane is 100 km away, in the direction N60°E. The other is 160km away, at a direction of S50°E. How far apart are the two planes?

19. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 2 N S N60°E S50°E 50° 60° 100km 160km C B A

20. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 2

21. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law Ex. 2… In order to find how far apart the two planes are, we first have to find out the angle opposite the side of the line between the two planes that will be the third side of the triangle… We can use the supplementary angle rule… Angle BCA = 180°- 60°- 50°= 70°

22. 6.6 Adjusting the Pythagorean Theorem: The Cosine Law

23. Homework Thursday, January 9 th - 6.6 Cosine law applications Hwk p.568, #14-21, 24 & 26