One way.
Can we assume the corners are right angles?
If so, ...
The short height can be found: (h2)^2 + 10^2 = 20^2
h2 = 10*sqrt(3)
The tall height can be found: (h3)^2 + 10^2 = 30^2
h3 = 20*sqrt(2)
Put an Origin at the lower, lefthand corner. y-axis runs up the tall height. x-axis runs across the bottom.
The equation with positive slope is now obvious: y = x*sqrt(3)
The equation with negative slope is a little trickier. y = sqrt(2)*[20 - 2x]
From there, it's not TOO hard to find the point of intersection. Of course, for this problem, you don't really need the x-value. I get a height of 10.742 -- You tell me what the exact value is.