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: 10

Answer

A force of $2.8~tons$ holds the monolith on the causeway.

Work Step by Step

If the causeway is 500 ft longer, it doesn't affect the force required to hold the monolith. The force required depends on the angle of the causeway above the horizontal which is $2.3^{\circ}$ If the monolith weighed 10 tons more, the new weight of the monolith would be 70 tons. Let $F$ be the force directed up the hill that holds the monolith on the causeway. The monolith's weight of $70~tons$ 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 $70~tons$ as the hypotenuse of the triangle and the force $F$ opposite the angle of $2.3^{\circ}$. We can find the force $F$: $\frac{F}{70~tons} = sin~2.3^{\circ}$ $F = (70~tons)~sin~2.3^{\circ}$ $F = 2.8~tons$ A force of $2.8~tons$ holds the monolith on the causeway.
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