TT #4 · Parashas Vayeira · Passuk 18:2
He lifted his eyes and saw, and behold, three men were standing over him; he saw, and he ran toward them from the entrance of the tent, and he bowed to the ground.
Torah Temimah points to Bava Metzia 86b. E-Daf · Sefaria — Bava Metzia 86b
TT lemma: והנה שלשה אנשים.
“And behold, three men.” Who were these three men? Michael, Gabriel, and Raphael: Michael came to announce to Sarah, Raphael to heal Avraham, and Gabriel went to overturn Sedom.
Derash on the verse (Bavli sugya) — not a formal named middah of the 13. The three figures are identified by their later actions and by the principle that one angel is not given two tasks.
The three men were the angels Michael (to announce Yitzchak’s birth), Raphael (to heal Avraham), and Gabriel (to destroy Sedom); each had a single mission.