See Konstantine Zelator, [Integral Triangles][1] with one angle twice another, and with the bisector(of the double angle) also of integral length. The abstract says, "In Result 2 in Section 5, we offer 3-parameter formulas that describe the entire family of integral triangles $ABC$ with $\angle A=2\angle B$." 


  [1]: https://arxiv.org/abs/1208.0497