You don't give the metal thickness or the loads that the stresspoints are going to be holding. Is it aluminum or steel? These are important questions because it might not be your welding that is the issue, it could just be what the structure itself is capable of holding.
Also, it depends on the quality of the welds you make. If there's any question of safety I would weld triangle supports on the backside (if possible).
But anyway, I would say (because of the thinness of the "shelf" that it's just the "sheer" weight that's bearing down on the shelf - you prolly don't have to factor in any trig because the weight is so close to the welded part itself. This is all given the scale of the drawing in your picture.
But I'm more of a sheet-metal welder than structural welder.