A 68-year-old man with a 10-year history of hypertension (BP 165/95 mmHg today) presents to the emergency department with sudden-onset epistaxis from the right nostril. The bleeding is profuse and originates from the posterolateral wall of the nasal cavity. He denies trauma, recent nasal surgery, or use of anticoagulants. On examination, the bleeding point is not visible anteriorly. What is the most likely source of bleeding and the most appropriate initial management?