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: 28

Answer

$\theta = 104.48^{o}$ $\phi = 75.52$ c = 63.24

Work Step by Step

The following are the given values: a = 40 b = 60 d = 80 Using the Law of Cosines, we can find $\theta$: $cos(\theta) = \frac{40^{2} + 60^{2} - 80^{2}}{2(40)(60)}$ $\theta = 104.48^{o}$ Knowing that a parallelogram has $360^{o}$, we can find $\phi$: $\frac{360 - (104.48)(2)}{2} = 75.52$ $\phi = 75.52$ Using the Law of Cosines, we can find c: $c^{2} = 40^{2} + 60^{2} - 2(40)(60)cos(75.52^{o})$ c = 63.24 $\theta = 104.48^{o}$ $\phi = 75.52$ c = 63.24
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