Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 7 - Review Exercises - Page 352: 50


The hill makes an angle of $3.8^{\circ}$ with the horizontal.

Work Step by Step

Let $\theta$ be the angle the hill makes with the horizontal. The car's weight of $2800~lb$ is directed straight down. The force of $186~lb$ is directed up the hill at an angle of $\theta$ above the horizontal. We can draw a triangle with the $2800~lb$ as the hypotenuse of the triangle and the force of $186~lb$ opposite the angle $\theta$. We can find $\theta$: $sin~\theta = \frac{186}{2800}$ $\theta = arcsin(\frac{186}{2800})$ $\theta = 3.8^{\circ}$ The hill makes an angle of $3.8^{\circ}$ with the horizontal.
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