I'd try to catch that coyote alive. I mean, imagine the money you could make with a bicycle riding coyote!
As for the question. Yes, I would shoot at a coyote if I could, even if the distance and angle were at best, iffy.
A broadhead is more likely to kill a 30lb coyote on a bad hit in fairly short order than a 150lb deer. And honestly, I consider coyotes vermin. Kendall shot one on the property here with a .22 cb. Heard the 'whap' of the hit but the coyote ran off, leaving no blood. Neither one of us cared if the coyote later died later... as long as it didn't come back.
I also put poison out for rats that takes about 5 days to kill them. Don't lose sleep over that.
Every year I have dozens of carp pull off my arrow before getting all the way back to the boat. Sometimes, I'll still have their swim bladder or other important parts stuck to the point. Other than in a tournament where I wanted the fish for the competition... I don't weep for mortally wounded and lost carp.
So yeah, I have a value system for critters .......and some have value as targets and not much more. Sorry, but I don't care if that bothers some people.
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