Final answer:
The radial nerve controls movement and sensation on the thumb side of the hand by innervating the thenar muscles, which include the abductor pollicis brevis, opponents' pollicis, flexor pollicis brevis, and the adductor pollicis.
Step-by-step explanation:
The radial nerve is responsible for the movement and sensation of the posterior side of the arm and forearm, as well as the dorsum of the hand. It innervates the thenar muscles which include the abductor pollicis brevis, opponents' pollicis, flexor pollicis brevis, and the adductor pollicis. These muscles are primarily involved in the movements of the thumb, forming the thenar eminence and allowing for the intricate motions such as gripping and manipulating objects.
Considering the muscles it innervates, the radial nerve is primarily responsible for the movement and sensation on the thumb side of the hand, making option A the correct answer.