The mountain lies completely within the drainage of the Skagit River, Bacon Creek and Goodell Creek being tributaries of the Skagit. Two small glaciers are found below the east face and north faces, both of which are receding. The south ridge of Mount Triumph ends at a minor peak that has been called Thornton Peak (). On its south flank is a deep cirque that hold the Thornton Lakes, a chain of three lakes at to , the source of south-flowing Thornton Creek, another tributary of the Skagit River.