  In this paper, constructions of regular pentagon and decagon, and the
calculation of the main trigonometric ratios of the corresponding central
angles are approached. In this way, for didactic purposes, it is intended to
show the reader that it is possible to broaden the study of Trigonometry by
addressing new applications and exercises, for example, with angles 18{\deg},
36{\deg} and 72{\deg}. It is also considered constructions of other regular
polygons and a relation to a construction of the regular icosahedron.
