## Elementary Geometry for College Students (6th Edition)

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