This is interesting as the word 'sagacious' has or had two meanings as one of them is obsolete. The first meaning relates to the same word stem as the word 'sage' or wise man, which in the short story 'The Black Cat' by Edgar Allen Poe is intriguing. For example, the main character may start off as being nice and sensible (or sage) but becomes less and less so as the story develops. In this sense the cat could be seen as having more sense than the man - it has discernment whereas at the end of the story the man has lost all his as he reverts to his baser nature. The second obsolete meaning is also interesting as it refers to a keen sense of smell - which a cat undoubtedly has! Deciding on Poe's true meaning will surely set 'the cat among the pigeons' among Poe's reviewers!
In Edgar Allen's Poe's "The Black Cat" the cat is a menacing presence. In order to identify why Poe used the word sagacious to define the cat, one needs to know the meaning of the word and some synonyms. Words that are often used to replace sagacious include: Perceptive, sly, and foxy.
Synonyms for Sagacious include: "wise, sage, discerning, clever, intelligent, judicious, acute, sharp, keen, perspicacious."
A reader may not anticipate that a cat could be capable of being so cunning. The word sets the stage for events that will follow when the cat uses its cunning to torture the man.