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: 14

Answer

C = $15^{o}$ a = 53.54 b = 43.71

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 - 120 - 45 = 15 Therefore, C = $15^{o}$ Finding a: We can use the Law of Sines. $\frac{a}{sin(120^{o})} = \frac{16}{sin(15^{o})}$ Therefore, a = 53.54 Finding b: We can use the Law of Sines. $\frac{b}{sin(45^{o})} = \frac{16}{sin(15^{o})}$ Therefore, b = 43.71 In total: C = $15^{o}$ a = 53.54 b = 43.71
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