1. Triangle Warm-up Can the following side lengths be the side lengths of a triangle?

2. Law of Sines and Law of Cosines

3. Solving Triangles Flow Chart

5. Law of Sines If you know the measures of two angles and one side of a triangle, you can find the other two sides of the triangle by using the Law of Sines In other words, if you are given ASA or AAS, use the Law of Sines.

6. Let’s Discover the Law of Sines 1)Find h in terms of a and the sine of an angle 2)Find h in terms of b and the sine of an angle 3)Use algebra to show Use Triangle ABC

7. Let’s Discover the Law of Sines 4)Find k in terms of c and the sine of an angle 5)Find k in terms of b and the sine of an angle 6)Use algebra to show Use Triangle ABC

8. Law of Sines For a triangle with angles A, B, and C and sides of lengths a, b, and c (a opposite A, b opposite B, and c opposite C),

9. Example 1 Solve the triangle.

11. Example 2 Solve the triangle and find the area.

12. Example 3 Solve the triangle and find the area.

13. Law of Cosines

14. For any triangle with sides of lengths a, b, and c, and with C the angle opposite the side with length c,

15. Example 4 Solve the triangle and find the area.

16. Example 5 Solve the triangle and find the area.