Below is part of a post I found on predatormasters by stiff neck. It is a great thread and the whole thing can be read here
http://www.predatormastersforums.com/ubbthreads/showflat.php?Cat=0&Number=53011853&page=0&fpart=1&vc=1 but I wanted to share part of it here.
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Coyotes offer us a million different shot angles, so let's just take a typical broadside shot to use as an example to keep things simple. Before we continue any further, look at this first picture and tell me where you'd put your shot.

Ok, now that you have chosen your shot placement, you may continue reading.
There are a thousand warnings on hunting forms like this one to stay away from the front shoulder or else the bullet will "splash" and you'll probably end up with a runner. However, there are a lot of coyote hunters, especially new hunters, who do not know where the shoulder really is. Many incorrectly think this is the shoulder due to the coyote's shape and fur color:

So they pick a spot "just behind the shoulder" and aim somewhere around here:

I bet a lot of hunters here chose that yellow dot at their aiming point. Yes? That is probably a lethal shot, but it may not be the best location to aim at. If you could peel the skin back, this is what you'd see below your aiming spot:

If you aim "just behind the shoulder" like the above diagrams show, you're really aiming at the very rear portion of the lungs and the liver. Clipping the lungs results in spins and runoffs.
If you're having problems with dogs that run away, perhaps you should consider altering your shot placement.
Let's go back and start over. Here's the same coyote standing broadside.

Where is his shoulder? Right about here:

I don't have as many kills under my belt as others do, but I do have an extremely high rate of DRT's. That's my goal every time I go out. I credit very careful shot placement combined with caliber/bullet selection.
Where do I aim? I draw a line down the neck and another line up the front leg. It is very simple to visualize these lines in the field. The spot where those lines meet is the magic death zone.

Why is that the magic spot? That's where all the goodies are! Look under the skin:

With a fragmenting bullet, you'll destroy the heart and severely damage at least one lung, probably both. I've found that even slightly quartering to, or slightly quartering away, this shot is lights out with my 223 and 40gr Vmax reloads. Bang-flop, lights out! When I pick them up, you can hear the vitals sloshing around.
Even if you hit the front leg (femur) on a shot quartering towards you, you'll still blast right thru it and destroy the heart even with a light bullet. I'd still recommend staying away from the shoulder blade, but I have never hit one yet so I don't have any personal experience there.
You never know how a coyote is going to approach you, or what angle you're going to be presented with for a shot, but there are things you can do to better your odds. Practicing with your equipment from field positions, knowing your limitations, careful stand selection and your position on the stand, and stopping coyotes for the shot are helpful.
Don't aim "at" a coyote, aim smart, aim for his vitals. Now, let's go out there and DRT some coyotes!
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