Elementary Geometry for College Students (7th Edition)

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

Chapter 11 - Section 11.1 - The Sine Ratio and Applications - Exercises - Page 505: 39b


$d = 2s \times sin54^{\circ} $

Work Step by Step

We know that each angle of a pentagon is 108 degrees. Thus, the bisected angle is 54 degrees, making the other angle 36 degrees. Thus, we solve for length of half of the diagonal, which we will call m: $sin54^{\circ} = \frac{m}{s} \\ m = s \times sin54^{\circ} $ Since d is twice m, this means: $d = 2s \times sin54^{\circ} $
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