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: 49

Answer

The magnitude of the resultant force is 533.5 N

Work Step by Step

Let $a = 250~N$ Let $b = 450~N$ Let angle $\theta = 85^{\circ}$ We can use the parallelogram rule to find $c$, the magnitude of the resultant force: $c = \sqrt{a^2+b^2+2ab~cos~\theta}$ $c = \sqrt{(250~N)^2+(450~N)^2+(2)(250~N)(450~N)~cos~85^{\circ}}$ $c = \sqrt{284610.04~N^2}$ $c = 533.5~N$ The magnitude of the resultant force is 533.5 N
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