The author develops a trigonometry for arbitrary irreducible Riemannian symmetric spaces of non-compact type. The geometry of a Riemannian space \(S\) is intimately connected with the geometry of its isometry group which is a semi-simple Lie group. Thus in the study of symmetric spaces the rich structure theory of semisimple Lie groups can be used. Geometric configurations of points in \(S\) are here expressed using group-theoretic properties of the Weyl chambre bundle. The study of geodesic triangles leads to invariants which allow to define the sides and the angles, respectively the congruence classes of marked regular geodesic triangles. As one of main results, the generalized laws of cosines and of sines are obtained. General concepts are illustrated in the space of Euclidean structures on \(\mathbb{R}^ n\).