Final answer:
The muscles responsible for elevating the ribs during inhalation to increase the thoracic cavity's dimensions are the external intercostal muscles.
Step-by-step explanation:
The muscles that extend from a superior rib inferomedially to the adjacent inferior rib and are responsible for elevating the ribs during inhalation, thereby increasing the transverse dimensions of the thoracic cavity, are the external intercostal muscles. These muscles aid in the inspiration of air by raising the rib cage when they contract, which in turn expands the thoracic cavity. Contrarily, the internal intercostal muscles are involved in expiration as they draw the ribs together to constrict the rib cage. The internal intercostals are located just beneath the external ones and, together with the innermost intercostal muscles, they help in changing the dimensions of the rib cage for efficient breathing.