In this note I give the important trigonometric relations between the Brocard and Steiner angles of the cross-section of a triangular prism and the angle which the plane of this cross-section makes with the plane cutting the prism in an equilateral triangle. To facilitate a comprehension of the whole problem, I also give a complete and brief solution of the known problem for the equilateral section of the prism, deducing the equations of the equilateral case from the equations for the general case in which the section is a triangle similar to a given triangle.