Adjective
1. (of a bad, difficult, or unwelcome situation or phenomenon) present or experienced to a severe or intense degree.
2. having or showing a perceptive understanding or insight; shrewd.
3. (of an angle) less than 90°.
Think of "A cute" angle. An acute angle is sharp and less than 90 degrees. This can remind you of the "sharpness" in the meanings – acute pain is sharp, acute understanding is sharp.