Where do the first branches of the aorta at its base lead?

Answer:

This is a perennial trick question in Anatomy class. The first branches of the aorta (technically, the ascending aorta) are the right & left coronary arteries, which supply the heart.

Many anatomy students spend so much effort learning the asymmetry of the aortic arch branches, and will misread the question. Here, this question's phrase "aorta at its base" actually provides a clue; without that, it's more misleading.

The first branch to leave the aortic arch is the brachiocephalic artery (a/k/a innominate artery). This branch splits into two major arteries: the right subclavian artery (which soon splits into arteries that supply the right neck and thorax) and the right common carotid artery (which supplies the right side of head and neck).

The next artery to stem from the aortic arch is the left common carotid artery (which supplies the right side of head and neck, though it basically supplies different muscles) and the left subclavian artery.