Trigonometry (10th Edition)

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

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.4 Vectors, Operations, and the Dot Product - 7.4 Exercises - Page 330: 53

Answer

The magnitude of the resultant force is 94 lb

Work Step by Step

Let $a = 40~lb$ Let $b = 60~lb$ Let angle $\theta = 40^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(40~lb)^2+(60~lb)^2+(2)(40~lb)(60~lb)~cos~40^{\circ}}$ $c = \sqrt{8877.01~lb^2}$ $c = 94~lb$ The magnitude of the resultant force is 94 lb
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