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 11.2 - The Cosine Ratio and Applications - Exercises - Page 512: 35

Answer

13.1

Work Step by Step

When we break a regular decagon into 20 separate right triangles, each triangle has an angle of 18 degrees in it. Using this angle and the fact that the apothem is 12.5 inches, we find: $cos18^{\circ}=\frac{12.5}{r} \\ r = \frac{12.5}{cos18^{\circ}} = 13.1$
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