We consider the inverse spectral problem for the Laplace operator on triangles with Dirichlet boundary conditions, providing numerical evidence to the effect that the eigenvalue triplet (?1,?2,?3) is sufficient to determine a triangle uniquely. On the other hand, we show that other combinations such as (?1,?2,?4) will not be enough, and that there will exist at least two triangles with the same values on these triplets.