Final answer:
The most suspicious diagnosis is aortic aneurysm.
Step-by-step explanation:
Based on the patient's medical history of hypertension and vascular disease, along with the presenting symptoms of tearing abdominal pain, low blood pressure, tachycardia, and abdominal rigidity and distention, the most suspicious diagnosis would be aortic aneurysm. Aortic aneurysm is a potentially life-threatening condition characterized by the weakening and bulging of the aorta, which can lead to abdominal pain and rupture, causing hypovolemic shock and potentially fatal hemorrhage.