Originally Posted by
skeeter draw in the altitude from the end of the side of length 6 perpendicular to the side of length 15 ... a 30-60-90 triangle is formed with hypotenuse length 6.
determine the length of the altitude, $\displaystyle a$ using the known side ratios of a 30-60-90 triangle.
another right triangle is formed with legs of length "$\displaystyle a$" and $\displaystyle b = 12$.
the hypotenuse of that right triangle is the short diagonal ... use Pythagoras to find its length.
next time, please be sure to include all information about a problem, especially what methods can be used to solve it.