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: 40

Answer

$13.7,7.11$

Work Step by Step

First converting the angle to decimal degrees: $27^{\circ}30'=27\frac{30}{60}=27.50^{\circ}$ 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 $|\textbf{v}|=15.4$ and $\theta=27.50^{\circ}$ in the formulas above, $x=15.4\cos27.50^{\circ}\approx13.7$ $y=15.4\sin27.50^{\circ}\approx7.11$ Therefore, $|\textbf{v}|=\langle 13.7,7.11 \rangle$
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