2. Notes Over 8.1 Solving Oblique Triangles To solve an oblique triangle, you need to be given one side, and at least two other parts (sides or angles). 4 cases for oblique triangles A B C a b c 1. Two angles and any side (AAS or ASA) 2. Two sides and an angle opposite one of them (SSA) 3. Three sides (SSS) 4. Two sides and their included angle (SAS) The first two cases use Law of Sines, the last two will use the Law of Cosines.

3. Notes Over 8.1 Law of Sines If ABC is a triangle with sides a, b, c, then according to the law of sines, or

4. The AAS or ASA Case Solve ∆ABC Find:

5. The AAS or ASA Case Solve ∆ABC Find:

6. Notes Over 8.1 The Ambiguous Case (SSA) Consider a triangle where you are given a, b, and A A a b If the height of the triangle h were equal to a, then it would be a right triangle. If a < h, then there would be no triangle. h a A is acute If a > b, then there would be one triangle. a If h < a < b, then there would be two triangles. a a

7. Notes Over 8.1 The SSA Case – One Triangle Solve ∆ABC Find: Since a > c, one triangle.

8. The SSA Case – Two Triangles Solve ∆ABC Find h. Since a < h, no triangle.

9. The SSA Case – Two Triangles Solve ∆ABC Find h. Since h < a < b, two triangles

10. Area of an Oblique Triangle For any triangle, given two sides and the included angle 6.Find the area of a triangular lot having two sides of lengths 90 meters and 52 meters and an included angle of 102 o.

11. Notes Over 8.1 Pg. 588, 8.1 #1-18 all