Which of the following injections is needed to anesthetize the maxillary posterior teeth?

To anesthetize the maxillary posterior teeth, particularly the first, second, and third molars, the posterior superior alveolar (PSA) injection is the most effective choice. This injection targets the PSA nerve branches that innervate the maxillary molars and their associated buccal soft tissues.

The PSA injection is typically administered in a specific area on the maxilla, near the maxillary tuberosity, which allows for the anesthetic agent to block the sensory nerves supplying the posterior maxillary teeth. This makes it quite successful for achieving profound anesthesia of the molars, including the maxillary sinus region surrounding these teeth.

In contrast, the inferior alveolar nerve block is intended for the mandible and would not affect the maxillary posterior teeth. The middle superior alveolar (MSA) is used to anesthetize the maxillary premolars and possibly the mesiobuccal root of the first molar, while the greater palatine (GP) injection provides numbness to the hard palate but does not directly anesthetize the teeth. Therefore, the PSA injection is the designated method specifically for the posterior maxillary teeth, making it the correct option for this question.