tranquilizers dont work like the movies also, its not like you just have a gun where you shoot something and it immediately falls down asleep
they would have to mix the solutions (you have to adjust for species and weight, and it goes bad when mixed, so you have to do a fresh one for each shot), then you shoot it. but it doesnt just fall down asleep, they freak out from being shot and run away for 20 minutes or so until slowing down and sleeping
if the dog was in an area where they couldnt afford to have a freaked out dog running around for 20 minutes, tranquilizers werent a choice