**Core Concept**
The underlying principle being tested is the knowledge of peripheral nerve anatomy and function, specifically the **radial nerve** and its distribution. The **radial nerve** is responsible for wrist and finger extension, as well as sensation on the dorsum of the hand.

**Why the Correct Answer is Right**
The **radial nerve** injury leads to weakness in extending the wrist, fingers, and thumb, while sparing elbow extension, which is consistent with the patient's presentation. The loss of sensation on the lateral half of the dorsum of the hand also points towards **radial nerve** damage. The injury is likely located in the arm, given the specific pattern of deficits.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because it does not match the specific pattern of deficits associated with the **radial nerve**.
**Option B:** Incorrect as it does not correlate with the clinical presentation.
**Option C:** Incorrect because the clinical findings do not align with the function of this nerve.
**Option D:** Incorrect as the description does not fit the typical presentation of an injury to this nerve.

**Clinical Pearl / High-Yield Fact**
A key point to remember is that the **radial nerve** can be injured at various levels, but the clinical presentation will vary depending on the location of the injury. Injuries at the level of the arm will result in deficits in wrist and finger extension, as well as sensory loss on the dorsum of the hand.

**Correct Answer:** D. Radial nerve, in the arm, forearm, or at the elbow.