Final answer:
A failed rift arm that extends into the craton, forming a narrow, elongate basin, is known as a graben, which is option A in the given choices.
Step-by-step explanation:
A failed rift arm is a geological feature indicative of an area where continental rifting began but did not progress to the point of creating an ocean basin. This structure can form an elongate basin known as a graben, which is an area of land that has dropped down between two faults, creating a valley. Comparatively, a horst is an elevated block of land between faults, a sag basin is formed by the extension of the continental crust, and a foreland basin forms adjacent to mountain belts due to crustal thickening. The correct answer to the student's question is A. Graben, which is a narrow, elongate basin that extends into the craton, in line with the description provided in the question.