**Core Concept**
The triangular interval of the arm is an anatomical space bounded by the humerus, teres major, and long head of triceps brachii. It is a significant region for the passage of nerves and blood vessels in the arm.

**Why the Correct Answer is Right**
The radial nerve is a branch of the brachial plexus that passes through the triangular interval of the arm. It is responsible for innervating the extensor muscles of the arm and forearm. The radial nerve originates from the posterior cord of the brachial plexus, which is formed by the C5-C8 spinal nerves. As it passes through the triangular interval, it is closely associated with the radial artery and the deep brachial artery.

**Why Each Wrong Option is Incorrect**
**Option A:** The axillary nerve, on the other hand, passes through the quadrangular space, not the triangular interval. It is responsible for innervating the deltoid and teres minor muscles.

**Option B:** The median nerve passes through the cubital tunnel at the elbow, not the triangular interval. It is responsible for innervating the flexor muscles of the forearm and the thenar muscles of the hand.

**Option C:** The ulnar nerve passes through the cubital tunnel at the elbow and the Guyon's canal at the wrist, but not through the triangular interval. It is responsible for innervating the flexor muscles of the forearm and the intrinsic muscles of the hand.

**Clinical Pearl / High-Yield Fact**
The radial nerve is at risk of injury during procedures such as humeral fractures, dislocations, and surgical interventions in the region. Knowledge of the anatomy of the radial nerve and its passage through the triangular interval is crucial for avoiding nerve damage and ensuring proper healing outcomes.

**✓ Correct Answer: A. Radial nerve**