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: 15

Answer

C = $83^{o}$ a = 0.62 b = 0.51

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 a, b, and C. Finding C: Since we are given 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$. 180 - 55 - 42 = 83 Therefore, C = $83^{o}$ Finding a: We can use the Law of Sines. $\frac{a}{sin(55^{o})} = \frac{0.75}{sin(83^{o})}$ Therefore, a = 0.62 Finding b: We can use the Law of Sines. $\frac{b}{sin(42^{o})} = \frac{0.75}{sin(83^{o})}$ Therefore, b = 0.51 In total: C = $83^{o}$ a = 0.62 b = 0.51
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