If you shoot the BG in the back, then by reasonable assumption that would indicate you are at some degree of angle to his rear...And not to his side or front angles.
We're talking 15 degrees max.
So being to his rear as within a 15 degree angle how can you tell with surety that the bore of the gun is faced at the third party and not for example at some inanimate object such as say the floor or ceiling, which does happen?
As well how can you tell if the BGs finger is on the trigger?
This latter item is highly important. If his finger is on the trigger and you fire into his "back", you cannot at all with any reason be sure that he will not secondarily discharge that weapon as into the third party person that you believe to be on the opposite end of the bore (be that belief accurate or not).
No, I would not shoot a person such as in this scenario in the back.
If pressed though and that my only available option were to either fire or in the _IMMEDIATE_ watching the BG execute the confirmed & known GG third party ( I say confirmed & known because it cannot always be assumed that said person is in fact a GG), then I _might_ target the head with a fine accuracy aimed shot. Just know if you miss or that round penetrates the head (or his back) that you have a GG third party just on his other side as within handgun engagement range. Very high risk.
I think my first thought would be rather than to shoot to instead make a noise and draw the BGs attention as away from the third party.
Toss a can or some other object at hand as in a direction away from the third party AND as from me for the BG to turn and look toward if even momentarily allowing for a better higher chance of success shot by me, the interjector.
One must think things through, completely, before acting.
My default thought would be to 1) Get myself (!) to concealment if not cover, 2) Assess and observe looking not just at the active threat but for his backup (hyena always hunt in pairs & groups), 3) Determine the relative degree of seriousness by the active threat(s) because he having a weapon of some sort is not on it's own a clear determinant of intent to actually use it, and 4) What is the attitude and response from those around me including not just the immediate victim but others in my air space watching him, them _and_ ME too!
This is not simple 1+1=2 math.
It is instead very often a pop quiz featuring trigonometry...
- Janq