1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Use the law of cosines to solve triangles. 14.2 The Law of Cosines

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Term law of cosines 14.2 The Law of Cosines

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Law of Cosines 14.2 The Law of Cosines a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Solving a Triangle 14.2 The Law of Cosines SSSlaw of cosines, then law of sines SSAlaw of sines (ambiguous) SAAlaw of sines ASAlaw of sines SASlaw of cosines, then law of sines AAAnot possible GivenUse

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the law of cosines to solve triangles. 14.2 The Law of Cosines a = 42, b = 35, C = 61º c 2 = a 2 + b 2 – 2ab cos C c 2 = 42 2 + 35 2 – 2(42)(35) cos 61º c 2 = 1563.66 c  39.54

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the law of cosines to solve triangles. 14.2 The Law of Cosines a = 42, b = 35, C = 61º c  39.54 sin A 42 sin 61º 39.54 = 42 sin 61º 39.54 A =  68.3º sin B 35 sin 61º 39.54 = 35 sin 61º 39.54 B =  50.7º TOC