1. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Objective Solve mathematical and real-world problems by using the law of sines. 14.1 The Law of Sines

2. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Glossary Terms area of a triangle law of sines 14.1 The Law of Sines

3. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Area of a Triangle 14.1 The Law of Sines K = area K = bc sin A 1 2 K = ac sin B 1 2 K = ab sin C 1 2

4. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Law of Sines 14.1 The Law of Sines sin A a sin B b sin C c ==

5. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Rules and Properties Summary of the Law of Sines 14.1 The Law of Sines GivenYou Can SASfind the area of a triangle ASAsolve a triangle SAAsolve a triangle SSAdefine 0, 1, or 2 triangles

6. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the law of sines to solve triangles. 14.1 The Law of Sines A = 61º, C = 38º, a = 12 sin A a sin C c = 12 sin 38º sin 61º c = sin 61º 12 sin 38º c =  8.4

7. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Use the law of sines to solve triangles. 14.1 The Law of Sines A = 61º, C = 38º, a = 12 sin A a sin B b = 12 sin 81º sin 61º b = sin 61º 12 sin 81º b =  13.6 B = 180º – 61º – 38º = 81º c  8.4

8. Copyright © by Holt, Rinehart and Winston. All Rights Reserved. Key Skills Determine whether the given SSA information defines 0, 1, or 2 triangles. 14.1 The Law of Sines a = 6, b = 3, and B = 120º sin A a sin B b = sin A 6 sin 120º 3 = sin A = 6 sin 120º 3  1.7321 There is no angle whose sine is 1.7321, so no triangle can be formed. TOC