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 11.3 - The Tangent Ratio and Other Ratios - Exercises - Page 520: 41

Answer

4.13

Work Step by Step

When a pentagon is broken into 10 separate right triangles. each triangle will have an angle of 36 degrees in it, and each triangle will have a leg equal to half of the length of a side. Thus, we find: $tan(36^{\circ}) = \frac{6/2}{a} \\ a = \frac{3}{tan(36^{\circ})} =4.13 $
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