Final answer:
The extensor muscles in the superficial posterior compartment of the forearm would be affected if the posterior interosseous branch of the radial nerve were to become entrapped.
Step-by-step explanation:
The muscles that would be affected if the posterior interosseous branch of the radial nerve were to become entrapped are the extensor muscles in the superficial posterior compartment of the forearm. The extensor muscles in the superficial posterior compartment of the forearm would be affected if the posterior interosseous branch of the radial nerve were to become entrapped.
These muscles include the extensor radialis longus, extensor carpi radialis brevis, extensor digitorum, extensor digiti minimi, and extensor carpi ulnaris. The entrapment of the nerve can lead to weakness, pain, and limited movement in these muscles.