Final answer:
The Tyrannosaurus Rex is hierarchically classified within Vertebrata, Reptilia, and Archosauria, reflecting its evolutionary lineage within theropods and its status as an ancestral group to birds.
Step-by-step explanation:
The Tyrannosaurus Rex is part of the following hierarchical classification: B. Vertebrata, Reptilia, Archosauria. This is consistent with the understanding that T. Rex is a theropod dinosaur, which is a group ancestral to birds and part of the larger archosaur clade.
Theropod dinosaurs are part of a group known as diapsids, specifically within the Archosauria, which includes crocodilians, pterosaurs, dinosaurs, and modern birds. Birds evolved from a branch of theropod dinosaurs within this clade. The vertebral column is a characteristic of Vertebrata, a subphylum of Chordata that includes animals with backbones. T. Rex, being a vertebrate, holds a backbone and is deeply rooted within the Reptilia class due to its mesozoic dinosaur lineage.
Dinosaurs proliferated during the Mesozoic era, commonly referred to as the 'Age of Reptiles', and the T. Rex is part of this diverse and dominant group. The correct classification reflects the evolutionary history, showing that birds are an extant form of certain theropod dinosaurs rather than a separate class within the overall amniote family tree.