Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 7 - Applications of Trigonometric Functions - Section 7.4 Area of a Triangle - 7.4 Assess Your Understanding - Page 565: 36

Answer

$326.7$ square feet

Work Step by Step

The radius of the circle or sector is equal to: $r=\dfrac{diameter}{2}=12$ A sector with a central angle measure of $100^o$ was removed; therefore, the angle surrounded by the tent becomes: $360^{\circ}-100^{\circ}=260^{\circ}$ The area of sector $K_{s}$ can be determined by the formula: $K_{s}=\dfrac{\theta}{360}\cdot \pi \cdot r^2$, where $\theta$ is in degrees So, $K_{s}=\dfrac{260}{360} ( \pi)(12^2) \approx 326.7$ square feet
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