Triangles are an ever-present feature in nature, which the building construction industry duly echoes. However, an exact expression intended to supply the radiant field of any triangle in an upright or inclined position has not been identified by previous research. In this case, the author has been able to solve, via direct integration, the canonical expression of radiative transfer. This result alone confers a myriad of possibilities, that had been inconceivable before, for studying in detail the three-dimensional heat-transfer behavior of volumes and figures in which triangles manifest, such as fins, windows, roof-gables and louvers of various kinds. Typically, shading devices, when tilted, give rise in their extremes to rhomboidal shapes which were difficult to take into account or had to be subject to discretization and subsequent Monte Carlo methods in order to perform an approximate calculation of their emissions. This implied a lengthy and inexact procedure that induced many errors and consumed computing time. We can now avoid all these former downsides due to the advances hereby presented. As this novel expression can be converted into an algorithm, it will be advantageously employed for simulation. This significant finding dovetails into the intricate puzzle of radiated heat and we believe that its consequences will greatly affect the conception and design of HVAC devices, aircraft manufacturing and specifically the building or lighting industries, among others.