We prove the conjecture posed by Laugesen and Siudeja that the second Dirichlet eigenvalue is simple for any non-equilateral triangle. A central challenge lies in separating the second and third eigenvalues for nearly equilateral triangles and nearly degenerate triangles. To resolve this, for the nearly equilateral case, we estimate the growth rate of eigenvalues in the neighborhood of the equilateral triangle to control the spectral gap of clustered eigenvalues. For the nearly degenerate case, we propose quantitative estimates for the asymptotic behavior of the diverging eigenvalues.