1. Chapter 6 – Trigonometric Functions: Right Triangle Approach
Section Law of Sines
6.5 - Law of Sines

2. Law of Sines
Used for oblique triangles (triangles that do not contain right angles).
6.5 - Law of Sines

3. Law of Sines We have two possible cases for the law of sines.
Case 1 – One side and two angles (ASA or SAA)
Case 2 – Two sides and the opposite angle to one of those sides (SSA)
6.5 - Law of Sines

4. Definition Law of Sines works when we have SAA or ASA.

5. Solving Using SAA
Solve the triangles below: a) b)
6.5 - Law of Sines

6. Solving Using ASA
Solve the triangles below: a) b)
6.5 - Law of Sines

7. The Ambiguous Case (SSA)
SSA is called an ambiguous case because the given information can result in zero, one, or two triangles.
6.5 - Law of Sines

8. SSA – No Triangle
6.5 - Law of Sines

9. SSA – One Triangle
6.5 - Law of Sines

10. SSA – Two Triangles
6.5 - Law of Sines

11. Examples - SSA Solve ABC if A = 50, a = 10, and b = 20.
6.5 - Law of Sines

12. Examples - SSA Solve ABC if A = 40, a = 54, and b = 62.
6.5 - Law of Sines

13. Example – pg. 474
6.5 - Law of Sines

14. Example – pg. 474
6.5 - Law of Sines

15. Example – pg. 474
6.5 - Law of Sines

16. Example – pg. 475
6.5 - Law of Sines

17. More Practice
Sketch the triangle. Use the Law of Sines to solve for all possible triangles that satisfy the given conditions.
6.5 - Law of Sines