Law of Cosine Chapter 8.3

Law of Sine too, but…… Law of Cosine If the triangle is not a right triangle, we have 4 case scenarios to consider. Law of Sine too, but…… A S S S A A A S A Case 1: ASA or AAS Case 2: SSA Law of Cosine S S S A S S Case 3: SAS Case 4: SSS

Law of Cosine a² = b² + c² - 2bcCosα b² = a² + c² - 2acCosβ c² = a² + b² -2abCosγ S S S A S S Case 3: SAS Case 4: SSS

Solve the triangle. a² = b² + c² - 2bcCosα b² = a² + c² - 2acCosβ c² = a² + b² -2abCosγ β S c 2 α 60° A 3 S Side-Angle-Side

Solve the triangle. a² = b² + c² - 2bcCosα b² = a² + c² - 2acCosβ c² = a² + b² -2abCosγ γ S 2 b 45° α A 4 S Side-Angle-Side

Solve the triangle. a² = b² + c² - 2bcCosα b² = a² + c² - 2acCosβ c² = a² + b² -2abCosγ γ S S 4 3 β α 6 S Side-Side-Side

Solve the triangle. a² = b² + c² - 2bcCosα b² = a² + c² - 2acCosβ c² = a² + b² -2abCosγ γ S S 9 6 β α 4 S Side-Side-Side