Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 8 - Applications of Trigonometric Functions - 8.4 Area of a Triangle - 8.4 Assess Your Understanding - Page 545: 44

Answer

$442,815.6$ square miles

Work Step by Step

By Heron's formula, $K=\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\frac{a+b+c}{2}.$ Hence, here we have $s=\frac{1028+1046+965}{2}=1519.5$, Thus, $K=\sqrt{1519.5(1519.5-1028)(1519.5-1046)(1519.5-965)}\approx442,815.6$ square miles
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