If by 'effective' you mean that it will have the capability to dispatch the animal, a LONG way. .45 cal holes through one's anatomy tend to cause serious health problems.
Now.... what range can you effectively place those shots? That is probably not a question that can be answered by anyone else. A big variable is how well you can see, and use, the sights. Open sights can range from excellent to pathetic, and our skills at using them, basically the same description.
Trajectory is not in your favor either BUT is not the insurmountable problem it once was, with rangefinders being quite cheap these days.
Since you mentioned the 1886, I'm assuming that you don't have a scope on it.
So, it would probably be a very good idea to find a range where you can shoot a few targets beyond 100 yards, and see what sort of groups you can get. Paper plates on a stick make a nice impromptu target, and if you can keep the bullets on the plate, you should be able to keep them in the vital zone of a big game animal.
My guess is that 100 yards will be no problem with open sights, 200 will be pretty tough especially with field conditions (no bench rest and not as good of contrast with the critter & background), and somewhere in between you'll find a limit that you are comfortable with.