A 44-year-old cabinetmaker develops an ache in the upper right forearm over several weeks and then finds he cannot straighten his fingers. On examination he cannot extend any of the fingers or the thumb at the knuckle joints. When asked to extend the wrist it comes up strongly but deviates to the radial side. Elbow extension is strong. Sensation is normal everywhere in the hand and forearm.
Damage to which one of the following nerves best accounts for this cabinetmaker's finger drop?