Honestly? A lot of distance and a big game repeater rifle. .375 H&H, .50 BMG, .600 Nitro Express, something like that. Bears tend to be sprinters.
Angry bears are a lot like humans on PCP or other such drugs - you can actually cause enough damage for them to die but they keep going until their brains shut down for lack of oxygen. At "hiking through the woods" distances, about the only way to stop them before they get to you and kill you is to destroy the brain, or alternately use something that blows enough limbs off the bear (rocket or contact grenade or something) that it physically cannot pursue you.
" something that blows enough limbs off the bear (rocket or contact grenade or something) that it physically cannot pursue you."
Now that's a grisly scene....shades of The Holy Grail: "But I cut off your arms!" "No you didn't! No you didn't."
"Angry bears are a lot like humans on PCP or other such drugs - you can actually cause enough damage for them to die but they keep going until their brains shut down for lack of oxygen."
I was reading a book about a British Army officer who was hunting in Ceylon in the 1800's. He shot a rouge elephant with a large bore black powder rifle, the round went through the elephants heart (they found out later) but he still turned, ran a hundred yards and wiped out the beaters then fell over dead.