  The goal of the paper is to study the angle between two curves in the
framework of metric (and metric measure) spaces. More precisely, we give a new
notion of angle between two curves in a metric space. Such a notion has a
natural interplay with optimal transportation and is particularly well suited
for metric measure spaces satisfying the curvature-dimension condition. Indeed
one of the main results is the validity of the cosine formula on $RCD^{*}(K,N)$
metric measure spaces. As a consequence, the new introduced notions are
compatible with the corresponding classical ones for Riemannian manifolds,
Ricci limit spaces and Alexandrov spaces.
