Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 8 - 8.3 - Vectors in the Plane - 8.3 Exercises - Page 588: 94d

Answer

$582.39 \ mph$

Work Step by Step

We are given that $ \theta_{w} = 225^{\circ}$ and $\theta_{v} = 118^{\circ}$ We know that $v=||v|| \lt \cos \theta , \sin \theta \gt $ Thus, $w=60 \lt \cos 225^{\circ} , \sin 225^{\circ} \gt$ and $v=580 \lt \cos 118^{\circ} , \sin 118^{\circ} \gt$ Now, $w= \lt 60 \cos 225^{\circ} , 60 \sin 225^{\circ} \gt$ and $v= \lt 580\cos 118^{\circ} ,580 \sin 118^{\circ} \gt$ Therefore, $w+v= \lt 60 \cos 225^{\circ} , 60 \sin 225^{\circ} \gt + \lt 580\cos 118^{\circ} ,580 \sin 118^{\circ} \gt=\lt -229.867, 535.111 \gt$ So, $\sqrt {(-229.867)^2+(535.111)^2}=582.39 \ mph$
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