Final answer:
The nasolacrimal canal is the structure responsible for draining tears from the eyes into the nasal cavity.
Step-by-step explanation:
The anatomical structure responsible for draining tears from the eyes into the nasal cavity is the nasolacrimal canal. This canal is an extension of the lacrimal bone, starting at the lacrimal fossa and opening into the nasal cavity behind the inferior nasal concha. Tears produced by the lacrimal gland are conveyed to the lacrimal sac, and from this reservoir, they flow through the nasolacrimal duct to the nose. When there is an increased flow of tears, for example during crying, this can also result in a runny nose due to the anterior drainage alongside the usual posterior pathway.