Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 315: 46

Answer

The distance between the two ships is 745 miles.

Work Step by Step

Let $a = 402~mi$, let $b = 402~mi$, and let angle $C = 135^{\circ}40'$. We can use the law of cosines to find $c$, the length of the line opposite the angle $C$: $c^2 = a^2+b^2-2ab~cos~C$ $c = \sqrt{a^2+b^2-2ab~cos~C}$ $c = \sqrt{(402~mi)^2+(402~mi)^2-(2)(402~mi)(402~mi)~cos~135^{\circ}40'}$ $c = \sqrt{554395.6~mi^2}$ $c = 745~mi$ The distance between the two ships is 745 miles.
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