#### Answer

18.75 cm

#### Work Step by Step

A diagonal of a rectangle divides the rectangle into two (congruent) right triangles.
The diagonal is the hypotenuse (label with $c$), and
the side b=15.24 is adjacent to the angle $(A=35.65^{o})$ with the hypotenuse.
(SOHCAHTOA)
$\displaystyle \cos A=\frac{adj.side}{hypotenuse}$
$\displaystyle \cos A=\frac{b}{c}$. solve for c
$c=\displaystyle \frac{b}{\cos A}$
$ c=\displaystyle \frac{15.24}{\cos 35.65^{o}}\approx$18.7547889924$ \approx 18.75$ cm