Trigonometry · Challenge problem

From a point $A$ the angle of elevation to a stationary balloon is $40^\circ$. From point $B$, which lies $300$ m farther from the point directly below the balloon (with $A$, $B$, and that point collinear), the angle of elevation is $25^\circ$. Find the height of the balloon. Round to 2 decimal places (an exact answer is also accepted).