**Core Concept**
The anatomical snuff box is a triangular deepening on the radial, dorsal aspect of the hand, which is bounded medially by the tendon of the extensor pollicis longus muscle and laterally by the tendons of the extensor pollicis brevis and abductor pollicis longus muscles. This region is innervated by a specific nerve that provides sensation to the thumb.

**Why the Correct Answer is Right**
The nerve related to the anatomical snuff box is the **radial nerve**. The radial nerve descends down the arm, passing through the radial tunnel, and then divides into the superficial branch, which provides sensation to the dorsal aspect of the hand and the thumb, and the deep branch, which innervates the extensor muscles of the wrist and fingers. The superficial branch of the radial nerve is responsible for providing sensation to the anatomical snuff box.

**Why Each Wrong Option is Incorrect**
**Option A:** The median nerve, which runs along the palmar aspect of the hand, is not responsible for the sensation in the anatomical snuff box. It provides sensation to the palmar surface of the thumb, index, middle, and half of the ring finger.
**Option B:** The ulnar nerve, which runs along the medial aspect of the hand, is not responsible for the sensation in the anatomical snuff box. It provides sensation to the palmar surface of the little finger and half of the ring finger.
**Option C:** The musculocutaneous nerve, which is responsible for innervating the biceps and brachialis muscles, is not responsible for the sensation in the anatomical snuff box.

**Clinical Pearl / High-Yield Fact**
The superficial branch of the radial nerve can be compressed at the wrist, leading to a condition known as radial tunnel syndrome or radial neuropathy, which presents with pain and paresthesia in the thumb and first web space.

**Correct Answer:** C. Radial nerve.