copyright © by holt, rinehart and winston. all rights reserved. objective use the law of cosines to...
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Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Objective• Use the law of cosines to solve triangles.
14.2 The Law of Cosines
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Glossary Termlaw of cosines
14.2 The Law of Cosines
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Rules and PropertiesLaw of Cosines
14.2 The Law of Cosines
a2 = b2 + c2 – 2bc cos A
b2 = a2 + c2 – 2ac cos B
c2 = a2 + b2 – 2ab cos C
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Rules and PropertiesSolving a Triangle
14.2 The Law of Cosines
SSS law of cosines, then law of sines
SSA law of sines (ambiguous)
SAA law of sines
ASA law of sines
SAS law of cosines, then law of sines
AAA not possible
Given Use
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Key SkillsUse the law of cosines to solve triangles.
14.2 The Law of Cosines
a = 42, b = 35, C = 61º
c2 = a2 + b2 – 2ab cos C
c2 = 422 + 352 – 2(42)(35) cos 61º
c2 = 1563.66
c 39.54
Copyright © by Holt, Rinehart and Winston. All Rights Reserved.
Key SkillsUse 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
39.54A = 68.3º
sin B
35
sin 61º
39.54=
35 sin 61º
39.54B = 50.7º
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