Trigonometry (11th Edition) Clone

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

Chapter 3 - Radian Measure and the Unit Circle - Section 3.2 Applications of Radian Measure - 3.2 Exercises - Page 112: 47


$1116.1$ m$^{2}$

Work Step by Step

Step 1: The formula to be used here will be $A=\frac{1}{2}r^{2}\theta$ where $A$ is the area of a sector of a circle of radius $r$ and central angle $\theta$. Step 2: Substituting the values provided by the question into the formula, $A=\frac{1}{2}(29.2)^{2}(\frac{5\pi}{6})$ Step 3: $A=\frac{1}{2}\times(\frac{292}{10})^{2}\times(\frac{5\pi}{6})$ Step 4: $A=\frac{1}{2}\times(\frac{85264}{100})\times(\frac{5\pi}{6})$ Step 5: $A=\frac{5329\pi}{15}=1116.1$ m$^{2}$
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