Trigonometry (11th Edition) Clone

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

Chapter 7 - Applications of Trigonometry and Vectors - Section 7.3 The Law of Cosines - 7.3 Exercises - Page 320: 39


AB has a length of 257 m

Work Step by Step

We can use the law of cosines to find the length $AB$: $AB^2 = AC^2+BC^2-2(AC)(BC)~cos~C$ $AB = \sqrt{AC^2+BC^2-2(AC)(BC)~cos~C}$ $AB = \sqrt{(350~m)^2+(286~m)^2-(2)(350~m)(286~m)~cos~46.3^{\circ}}$ $AB = \sqrt{65981.34~m^2}$ $AB = 257~m$ AB has a length of 257 m
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