Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 13, Trigonometric Ratios and Functions - 13.6 Apply the Law of Cosines - 13.6 Exercises - Problem Solving - Page 893: 44

Answer

$\approx62.78$ square miles

Work Step by Step

The area of a triangle with sides $a,b,c$ is: $\sqrt{s(s-a)(s-b)(s-c)}$ where $s=0.5(a+b+c)$. Hence here $s=0.5(18+8+23)=24.5$, thus the area: $\sqrt{24.5(24.5-18)(24.5-8)(24.5-23)}\approx62.78$ square miles
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