Final answer:
The triceps brachii is the muscle that extends the forearm and is involved when there is pain around the olecranon process, which is part of the elbow.
Step-by-step explanation:
The muscle involved when a carpenter has pain around his olecranon process, which is part of the elbow, is likely the triceps brachii. The triceps brachii is the primary muscle responsible for extending the forearm. It originates from the scapula and upper humerus, and inserts onto the olecranon process of the ulna. When this muscle contracts, it extends the elbow joint, straightening the arm. In contrast, the biceps brachii is involved in flexing the forearm, the deltoid is mainly responsible for arm abduction, and the brachialis assists in forearm flexion.