When shooting medium or big game with an arrow.....hemorrhage is the mechanism that kills. And that is the reason for "double lunging" an animal with a broadhead. Deer, or other game, can run a long time with one good lung.

When shooting that same animal with a bullet....particularly from a high powered rifle....and using a cartridge and bullet of suitable construction and power......tissue damage to vital organs and shock are what kill. If you are confident that your choice of bullet can penetrate sufficiently to cause that damage to those vital organs.....the origination of the bullet entry and the angle are not significant. The only issue that matters.....was sufficient trauma to the vital organs accomplished. If in fact that trauma is inflicted....the animal will die both quickly and humanely.

It doesn't matter to the heart and/or lungs which direction the bullet came from! It could have came from behind the ribs, transversed the chest, and exited the front shoulder. It could have came from 180 degree opposite direction. It could have came from either side. It absolutely does not matter. All that matters....is that organs vital to life function were significantly traumatized. Medium and big game can be humanely dispatched with a bullet from any angle....as long as the vital organs are disrupted! (Failures in that regard come from a misapplication of appropriate bullet, and or caliber to get the job done correctly.) I've done it....and seen it done.....far to often to believe otherwise! I've seen animals the size of moose, shot "through and through" with bullets that transverse 3/4 or more of the length of the body. Use enough bullet and enough gun.....and you will humanely kill animals from any angle. (Except maybe elephants?)