A rational triangle is a Triangle all of whose sides are Rational Numbers and all of whose Angles are Rational numbers of Degrees. The only such triangle is the Equilateral Triangle (Conway and Guy 1996).
See also Equilateral Triangle, Fermat's Right Triangle Theorem, Right Triangle
Conway, J. H. and Guy, R. K. ``The Only Rational Triangle.'' In The Book of Numbers. New York: Springer-Verlag,
pp. 201 and 228-239, 1996.