the dynamics of a billiard ball on a triangular table can be studied by considering geodesic trajectories on an associated singular flat metric structure called a translation surface when the angles of the triangle are commensurable with pi. in the case of the isosceles right triangle, this surface is a torus, whose geodesic trajectories in any direction are either all periodic or all uniquely ergodic. triangles satisfying such a dichotomy are called lattice triangles, and our work contributes to the ongoing classification of such triangles. we make use of a number-theoretic criterion of mirzakhani and wright to classify such triangles with a large obtuse angle. this work is joint with anne larsen and chaya norton.