For three points $\vec{u}$,$\vec{v}$ and $\vec{w}$ in the $n$-dimensionalspace $\F_q^n$ over the finite field $\F_q$ of $q$ elements we give a naturalinterpretation of an acute angle triangle defined by this points. We obtain anupper bound on the size of a set $\cZ$ such that all triples of distinct points$\vec{u}, \vec{v}, \vec{w} \in \cZ$ define acute angle triangles. A similarquestion in the real space $\cR^n$ dates back to P. Erd{\H o}s and has beenstudied by several authors.
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