Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Review Exercises - Page 345: 37

Answer

The magnitude of the resultant force is 207.14 lb

Work Step by Step

Let $a = 100~lb$ Let $b = 130~lb$ The angle between $a$ and $b$ is $\theta = 52^{\circ}$ Then $C = 180^{\circ}-52^{\circ} = 128^{\circ}$ We can use the law of cosines to find $c$, which is the magnitude of the resultant force: $c^2 = a^2+b^2-2ab~cos~C$ $c = \sqrt{a^2+b^2-2ab~cos~C}$ $c = \sqrt{(100~lb)^2+(130~lb)^2-(2)(100~lb)(130~lb)~cos~128^{\circ}}$ $c = \sqrt{42907.198~lb^2}$ $c = 207.14~lb$ The magnitude of the resultant force is 207.14 lb
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