vintage US Navy officer or sailor uniform coat/jacket w/silver buttons

Old United States Navy uniform jacket with silver colored buttons and a shoulder patch. The buttons feature an eagle perched upon an anchor. We've been told that the shoulder sleeve patch is for an Engineering / Nuclear Power Petty Officer, but are not sure. This uniform coat has a label "DSA100-74-C-0240 - 55% Dacron Poly - 45% wool" and is marked as size 37R.

This uniform jacket measures about 17" long on the arm (from the armpit to the sleeve cuff), 40" around the chest (under the arms), 17" across the shoulders and 30" long from the base of the collar to the bottom in the back. It is in nice vintage condition.