For three points u, v and w in the n-dimensional space F n q over the finite field F q of q elements we give a natural interpretation of an acute angle triangle defined by these points. We obtain an upper bound on the size of a set Z such that all triples of distinct points u, v, w ∈ Z define acute angle triangles. A similar question in the real space R n dates back to P. Erdős and has been studied by several authors. 2000 Mathematics subject classification: primary 05B25; secondary 11T23, 52C10.