In right triangle $ABC$, angle $B$ is the right angle, the measure of angle $C$ is $\theta$, and the length of the hypotenuse $\overline{AC}$ is 16 units. If the area, in square units, of triangle $ABC$ can be represented by the expression $k\sin \theta \cos \theta$, where $k$ is a constant, what is the value of $k$?