An obvious example of realization of advantages of the generalized Fourier method GFD [1] over the classic one in solving of applied electrodynamics problems is the problem of hollow triangular cross section waveguide (Fig.1), whose envelope is considered to be a perfect conductor, while the inner medium is homogeneous. In the most cases, this model turns out to be satisfactory in practical calculations. If necessary, it can be made more accurate by accounting for the losses in the metal.