HMMT November 2010 U16

Triangle $A B C$ is given in the plane. Let $A D$ be the angle bisector of $\angle B A C$; let $B E$ be the altitude from $B$ to $A D$, and let $F$ be the midpoint of $A B$. Given that $A B=28, B C=33, C A=37$, what is the length of $E F$ ?