Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 321: 41


The angle opposite the longer diagonal is $163.5^{\circ}$

Work Step by Step

Let $a = 25.9~cm$, let $b = 32.5~cm$, and let $c = 57.8~cm$. We can use the law of cosines to find $C$, which is the angle opposite the longer diagonal: $c^2 = a^2+b^2-2ab~cos~C$ $2ab~cos~C = a^2+b^2-c^2$ $cos~C = \frac{a^2+b^2-c^2}{2ab}$ $C = arccos(\frac{a^2+b^2-c^2}{2ab})$ $C = arccos(\frac{25.9^2+32.5^2-57.8^2}{(2)(25.9)(32.5)})$ $C = arccos(-0.9586)$ $C = 163.5^{\circ}$ The angle opposite the longer diagonal is $163.5^{\circ}$
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