Just some thoughts on triangulating, they have to be right angled triangles.
The weight of the beam is interesting too, same with a tree, because the weight is dispersed over the length of the structure, so it's not like we put a 10T weight on top of a 100 pole, the bottom 10' of the beam weighs 1T etc, the beam weighs 1T per 10'.
If you have trouble visualising this concept or understanding it then think about it like this.
You have a 6' long 60lb crow bar. You have the tip stuck in the ground like you do for prying rocks etc. The crow bar is uniform weight and diameter the entire length so not too hard to use. Now imagine if the crow bar had the full 60lbs at the top and the rest was hollow tube ... it would be harder to use right? Now imagine the crow bar had the 60lbs of weight at the bottom 1' ... much easier to use. Hence similar to a tree/beam, centre of gravity matters too, so I really dont think straight forward triangulation is the answer.