A 3.7 cm aneurysm is not likely to
ruptureAortic rupture, chest x-ray
Ruptured eardrum
Tracheal/bronchial rupture soon, and the most important thing you need to make sure to prevent it from growing is to make sure his blood pressure NEVER gets above 130/80. It is the hypertension which is causing the aneurysm in all likelihood. There are rare instances in which it cuts off blood flow to a kidney and this secondarily causes a rise in blood pressure.
Surgery, in asymptomatic patients with aneurysms of this size is generally not warranted. They also tend to grow slowly if blood pressure is controlled, and require only yearly scans to follow up at this early stage.