The two tendons it consists of are the tendons of the muscles extensor pollicis brevis (which is closer to the palm), and extensor pollicis longus. The bodies of these muscles are quite thin, and are in the distal half of the forearm.
The radial artery runs on the floor of the anatomical snuff box. The carpal bones, scaphoid and trapezium can be palpated within the snuff box, so can the styloid process of the radius.