A 13-year-old boy is brought to the emergency depament after losing control during a motorbike race in which he was run over by several of the other racers. Physical examination reveals several cuts and bruises.He is unable to extend the left wrist, fingers, and thumb, although he can extend the elbow. Sensation is lost in the lateral half of the dorsum of the left hand. Which of the following nerves has most likely been injured to result in these signs, and in what pa of the arm is the injury located?