Mastering the Law of Sines: Solving Triangles & Applied Problems

1. Sullivan Algebra and Trigonometry: Section 8.2The Law of Sines • Objectives of this Section • Solve SAA or ASA Triangles • Solve SSA Triangles • Solve Applied Problems

2. All angles are acute Two acute angles, one obtuse angle If none of the angles of a triangle is a right angle, the triangle is called oblique. To solve an oblique triangle means to find the lengths of its sides and the measurements of its angles.

3. FOUR CASES CASE 1: One side and two angles are known (SAA or ASA). CASE 2: Two sides and the angle opposite one of them are known (SSA). CASE 3: Two sides and the included angle are known (SAS). CASE 4: Three sides are known (SSS).

4. The Law of Sines is used to solve triangles in which Case 1 or 2 holds. The Law of Sines is used to solve SAA, ASA or SSA triangles. Law of Sines

5. c b 5

6. b 12 a

7. 3 a 5

9. Two triangles!!

10. Triangle 1:

11. Triangle 2:

12. 3 5 a No triangle with the given measurements!