Elementary Geometry for College Students (7th Edition) Clone

Published by Cengage
ISBN 10: 978-1-337-61408-5
ISBN 13: 978-1-33761-408-5

Chapter 11 - Section 11.4 - Applications with Acute Triangles - Exercises - Page 528: 27

Answer

6.9

Work Step by Step

We use the Law of Cosines to find: $cos(60^{\circ})= \frac{-(6^2) + x^2 + 4^2 }{2(4)x} \\ 4x = x^2 - 20 \\ 0 = x^2 -4x -20$ We use the quadratic formula: $x= \frac{4 \pm \sqrt{16 - 4(-20)}}{2} \\ x=6.9$ (Note, x cannot be negative.)
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