A 32-year-old male labourer presents to the orthopaedic clinic with a 3-week history of weakness in wrist and finger extension following a fracture of the mid-shaft humerus sustained during a fall. On examination, he has wrist drop, inability to extend the thumb at the interphalangeal joint, and sensory loss over the dorsal first web space. The fracture has been managed conservatively. Which nerve is injured and at what anatomical location is the lesion most likely to occur?