A 35-year-old right-handed mechanic comes to the clinic with progressive right hand weakness. The patient frequently uses a screwdriver to perform his duties at work. On neurologic examination, sensation is preserved in his upper limbs. There is weakness on extension of the fingers and thumb in the right hand. Strength is otherwise intact throughout. Triceps reflexes are 2+ and bilaterally symmetric. The nerve affected in this patient was most likely injured at which of the following locations?