Final answer:
The diaphragm is the large muscle that contracts and increases the vertical dimensions of the thoracic cavity.
Step-by-step explanation:
The muscle that contracts to increase the vertical dimensions of the thoracic cavity is the diaphragm.
When the diaphragm contracts and flattens, the volume inside the pleural cavities increases, which decreases the pressure within them. This creates a lower pressure within the lungs than that of the atmosphere, causing air to be drawn into the lungs.
The external and internal intercostal muscles also play a role in changing the shape of the rib cage during inspiration and expiration, but they do not specifically increase the vertical dimensions of the thoracic cavity.