#### Answer

$a = 10cos 36^{\circ}$

#### Work Step by Step

When we break a polygon into 10 separate right triangles, each triangle has an angle of 36 degrees in it. Using this angle and the fact that the radius is 10 inches, we find:
$ cos 36^{\circ} = \frac{a}{10} \\ a = 10cos 36^{\circ}$