Odd rounded pyramid shape - how to calculate shape/size?

I am trying to figure out the "equation" or other means of finding the exact shape in the figure below. It's somewhat of a pyramid with a rectangular base, but the sides are curved rather than flat. I have found how to make the longer sides (simple half-circle) but the narrow two sides I can't quite figure out. The long edge is 40" and the shorter edge is 30".

Can anyone tell me exactly how to calculate the measurements/curves of the narrower side (third picture)?

NOTE: The narrow side in the third picture is really just a trial-and-error cut-out, no measurements or calculations were done to determine what it should look like.

Thanks!

http://farm3.static.flickr.com/2252/...0a726129d0.jpg

http://farm3.static.flickr.com/2082/...6c8b7d636a.jpg

http://farm3.static.flickr.com/2169/...98e1f9dfd5.jpg