Just as in the common triangle, solving the trihedral angle means getting some of the data and inferring the rest mathematically. Most such problems are solved by solid geometry and by spherical trigonometry. Here we present an approach which facilitates the handling of such problems. Moreover, the two basic theorems (namely, the law of sines and the law of cosines) of spherical trigonometry are derived as relatively simple by‐products of the general approach. Spherical trigonometry is a simple and vivid example of non‐Euclidian geometry and also a vital tool in navigation, astronomy and geodesy, etc. So it is worthwhile to consider it in the early stages of mathematical education.