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 329: 37

Answer

$47,17$

Work Step by Step

The horizontal component $x$ and vertical component $y$ of a vector $\textbf{v}$ having magnitude $|\textbf{v}|$ and direction angle $\theta$ are: $x=|\textbf{v}|\cos\theta$ and $y=|\textbf{v}|\sin\theta$ Substituting the values of $|\textbf{v}|=50$ and $\theta=20^{\circ}$, $x=50\cos20^{\circ}\approx47$ $y=50\sin20^{\circ}\approx17$ Therefore, $|\textbf{v}|=\langle 47,17 \rangle$
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