Treasure Bearing

A pirate buries a chest of gold somewhere in a square field that measures 50 paces by 50 paces. The spot is uniformly random: measured from the southwest corner, the chest's eastward distance $E$ and northward distance $N$ are independent $\text{Unif}(0,50)$ random variables. Standing at the southwest corner, the pirate draws an arrow pointing straight at the chest. Let $\theta$ be the angle between the arrow and the southern edge of the field (which runs due east).

What is the probability that $\theta$ exceeds $30^\circ$? Give an exact expression.