In this work we study the scattering of a plane incident wave by a semi-infinite impedance sector. We develop an approach that enables us to compute different components in the far-field asymptotics. The method is based on the Sommerfeld integral representation of the scattered wave field, on the careful study of singularities of the integrand and on the asymptotic evaluation of the integral by means of the saddle point technique. In this way, we describe the waves reflected from the sector, diffracted by its edges or scattered by the vertex as well as the surface waves.Surface waves