Final answer:
The third layer a needle penetrates from the outside of the skin in is the subcutaneous tissue or hypodermis, which comes after the epidermis and dermis.
Step-by-step explanation:
The third layer the needle penetrates when moving from the outside in is the subcutaneous tissue. Our skin is made of three general layers: the epidermis, which is the outermost layer; the dermis, which is directly below the epidermis and contains blood vessels, nerve endings, hair follicles, sweat glands, and sebaceous glands; and finally, the subcutaneous tissue, or hypodermis, which is the deepest and consists of fatty tissue containing blood vessels, nerves, and connective tissue. In the context of a novocaine injection at the dentist, after piercing the epidermis and dermis, the needle enters the subcutaneous tissue before reaching the target area to provide anesthesia.