Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.1 - Law of Sines - 8.1 Exercise - Page 566: 18

Answer

C = $42.35^{o}$ B = $77.66^{o}$ b = 10.15

Work Step by Step

Note: The Law of Sines is: $\frac{a}{sin(A)}$ = $\frac{b}{sin(B)}$ = $\frac{c}{sin(C)}$ To solve the triangle, we need to find B, b, and C. Finding C: We can use the Law of Sines. $\frac{9}{sin(60^{o})} = \frac{7}{sin(C^{o})}$ Therefore, C = $42.34^{o}$ Finding B: Since we know 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$. 180 - 60 - 42.34 = 77.66 Therefore, B = $77.66^{o}$ Finding b: We can use the Law of Sines. $\frac{9}{sin(60^{o})} = \frac{b}{sin(77.66^{o})}$ Therefore, b = 10.15 In total: C = $42.35^{o}$ B = $77.66^{o}$ b = 10.15
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