Formulas with triangles/descriptions for Law of the Cosines, Law of the Sines, and the Area Formula

2. Law of Cosines: Have: two sides, included angle Solve for: missing side ( missing side ) 2 = ( one side ) 2 + ( other side ) 2 – 2 ( one side )( other side ) cos( included angle ) c 2 = a 2 + b 2 – 2 a b cos C C c A a b B

3. Law of Cosines: C c A a b B a 2 + b 2 – c 2 2ab cos C = Have: three sides Solve for: missing angle Missing Angle Side Opposite Missing Angle

4. Law of Sines: C c A a b B Have: two angles, one side opposite one of the given angles Solve for: missing side opposite the other given angle Missing Side a sin A = b sin B

5. Ambiguous Case: ( Special Case of Law of Sines ) C c A a b B Have: two sides, angle opposite one of the given sides Solve for: missing angle opposite the other given side Missing Angle a sin A = b sin B

6. Area Formula: t C c A a b B Have: two sides, included angle K = a b sin C two sides included angle