Trust-region methods are fundamental to nonlinear optimization, but solving the trust-region subproblem exactly can be computationally expensive. This paper proposes Aries, a three-segment path approximation that extends the classical dogleg path while retaining comparable per-iteration work. We state the assumptions under which the usual trust-region sufficient-decrease argument applies and describe an adaptive rule for selecting the path parameters. Numerical experiments on the S2MPJ test set using Dolan–Moré performance profiles indicate that adaptive Aries is competitive with both fixed-parameter Aries and dogleg, with the precise ranking depending on whether CPU time or iteration count is measured.