Is every triangle with 3 rational angles (in degrees) similar to one with 3 integer-length sides?

Question

The same way right triangles have pythagorean triples, does every non-right class of similar triangles also have some integer triples, if we say that all the angles have to be rational numbers in degrees?

Are there other interesting results about integer triples if we relax/tighten the restrictions on the angle values?

Answer 1

No. Consider a triangle with angles 30, 60, 90.