Summary of Solving Triangles:

(given any three parts)

•SSS – Given 3 sides
1. Use Law of Cosines to find other 2 angles
2. Find 3rd angle by 180 minus two angles

•SAS – Given 1 angle & other 2 sides (not opposite side)
1. Use Law of Cosines to find the 3rd side and 2nd angle
2. Find 3rd angle by 180 minus two angles

•AAS or ASA – Given 2 angles & 1 side
1. Find 3rd angle by 180 minus two angles
2. Use Law of Sines to find other 2 sides

•SSA – Given 1 angle & 2 sides (one side opposite to the angle)
1. Using Law of Cosines:
       •Find the 3rd side, using the equation of the given angle
       •This will give a quadratic equation with graph that has 1, 2, or no solutions.
2. Use Law of Sines, determine if 1, 2, or no ∆s:
       •Given obtuse angle A:
              1.a > b                            - one triangle
              2.a < b                            - no triangle
       •Give acute angle A:              
              1.a > b                            - one triangle
              2.a < b  
                 •a > h (h < a < b)        - two triangles
                 •a = h                           - one triangle
                 •a < h                           - no triangle