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: 42

Answer

$198,132$

Work Step by Step

The formulas for 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 $|\textbf{v}|=238$ and $\theta=146.3^{\circ}$ in the formulas above, $x=238\cos146.3^{\circ}\approx-198$ $y=238\sin146.3^{\circ}\approx132$ Therefore, $|\textbf{v}|=\langle -198,132 \rangle$ Since the question requires magnitudes of horizontal and vertical components, the magnitude of horizontal component is $198$ and the magnitude of vertical component is $132$.
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