Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.5 Applications of Vectors - 7.5 Exercises - Page 336: 9

Answer

A force of $2.4~tons$ holds the monolith on the causeway.

Work Step by Step

Let $F$ be the force directed up the hill that holds the monolith on the causeway. The monolith's weight of $60~tons$ is directed straight down. The force $F$ is directed up the causeway at an angle of $2.3^{\circ}$ above the horizontal. We can draw a right angle triangle with $60~tons$ as the hypotenuse of the triangle and the force $F$ opposite the angle of $2.3^{\circ}$. We can find the force $F$: $\frac{F}{60~tons} = sin~2.3^{\circ}$ $F = (60~tons)~sin~2.3^{\circ}$ $F = 2.4~tons$ A force of $2.4~tons$ holds the monolith on the causeway.
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