In right triangle $DEF$, angle $E$ is the right angle, the measure of angle $F$ is $51^{\circ }$, and the length of $\overline{EF}$ is 15 units. If the area, in square units, of triangle $DEF$ can be represented by the expression $m\tan 51^{\circ }$, where $m$ is a constant, what is the value of $m$?