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: 53


$1885.0$ mi$^{2}$

Work Step by Step

First converting $135^{\circ}$ to radians: $135^{\circ}=135(\frac{\pi}{180})=\frac{3\pi}{4}$ radians The formula for the area of a sector of a circle having radius $r$ and central angle $\theta$ is $A=\frac{1}{2}r^{2}\theta$. Substituting the values of $r$ and $\theta$ into the formula: $A=\frac{1}{2}(40.0)^{2}(\frac{3\pi}{4})$ Solving through a calculator: $A=\frac{1}{2}(40.0)^{2}(\frac{3\pi}{4})\approx1885.0$ mi$^{2}$
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