Step 1: Read the attachments shown. Muscle A starts at the lateral epicondyle and supraepicondylar ridge of the humerus and ends on the dorsal base of the second metacarpal - the route of the extensor carpi radialis longus.
Step 2: Note its relations. Proximally it hides deep to the brachioradialis on the lateral forearm, a clue separating it from its neighbour.
Step 3: Confirm by action and nerve. It extends and abducts the hand at the wrist and is supplied by the radial nerve, consistent with a posterior-compartment extensor.
Step 4: Distractors fail: brachioradialis inserts at the radial styloid, flexor carpi radialis is an anterior-compartment flexor, and extensor carpi ulnaris reaches the fifth metacarpal for ulnar deviation. Muscle A is the extensor carpi radialis longus.
\[\boxed{\text{Extensor carpi radialis longus}}\]