I can't quite get my head around how a load, say 200lb, applied centrally, can result in more than 100lb at each tree. Is it because the 200lb is a vertical component being supported at an angle (alpha) which has both horizontal and vertical components? I think I'd need to work my way through the calcs. Its been a while!
I very much wish I could help you. As you imply, you can get there by feeling fine about the calculations, substituting identities. For it to be intuitive to me, however, I believe there must be a diagram of an implicit lever with an implied fulcrum point and ratio of load arm length and implied force-arm lengths.
I'm looking for that diagram. Can someone point to an URL with it?