Abstract: This paper discusses the solution of a group of two-order six elements rooted algebraic simultaneous equations set up by cosine law arising from the application example of subjectivity geometry^[1].By means of the implicit function theorem, this paper proves that there exists a unique real solution of those equations.Transforming this problem into an unconstrained nonlinear optimization problem, the solution can be found by known methods.4 numerical example by descent method is given.