You do the physics in your head and start to form a plan. Waiting for the dog to fall asleep was crossed off the list early on because this dog looks like they have a lot of energy and who knows how long before a dwarf comes wandering by.
If you don't throw the mantis meat far enough the dog will be alerted to your presence AND you won't be able to get past it.
If you throw the mantis meat in the corner of the tunnel you should have just enough time to slip past but there is the chance the dog will alert the fortress to your presence.
If you throw the meat to far, however, the dog will not be able to reach it and will turn it's attention back to you. If the chain is long enough, you may be able to trick the dog into hanging itself...
Last but certainly not least, you could throw the meat through the dogs skull. This has been known to work in the past and it is the most FUN option.
After dealing with the pupper you still have to choose your next hidding spot. You could start your way down the massive ramp, the tunnel to the left, or the tunnel straight ahead.
The tunnel on the right wall is sealed off.