Algebra and Trigonometry 10th Edition

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

Chapter 8 - 8.2 - Law of Cosines - 8.2 Exercises - Page 573: 36


A = $31.87^{o}$ C = $136.13^{o}$ c = 210

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, c, and C. Finding A: We can use the Law of Sines. $\frac{160}{sin(A^{o})} = \frac{63}{sin(12^{o})}$ Therefore, A = $31.87^{o}$ Finding C: Since we are have 2 other angles, we can use the fact that a triangle has angles that add to $180^{o}$. 180 - 31.87 - 12 = 136.13 Therefore, C = $136.13^{o}$ Finding c: We can use the Law of Sines. $\frac{63}{sin(12^{o})} = \frac{c}{sin(136.13^{o})}$ Therefore, c = 210 In total: A = $31.87^{o}$ C = $136.13^{o}$ c = 210
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