Let    and  It is proved that in a Euclidean plane, there is, up to congruence, at most one triangle  such that the side BC(resp., AB) has length a,  has radian measure a, and Dhas perimeter p. Conditions are given on a, a and pfor the existence of such D. If only pand one of a, aare specified, there exist infinitely many congruence classes of triangles with the specified properties. The only prerequisites for this note are elementary analytic geometry and differential calculus.

Euclidean geometry, triangle, perimeter, side-length, angle, right triangle, Law of Sines, quadratic equation, derivative.