A surveyor has taken measurements, $a$ ft, $b$ ft, and the angle $\gamma$ in degrees, as seen in the figure below.
If $a = 288$ ft, $b = 433$ ft, and $\gamma = 37^\circ$, find the distance across the lake.
The distance across the lake is $\boxed{}$ ft.
NOTE: Enter an answer correct to at least 4 decimal places.