## Triangle approximation

"The triples (a, b, c) in Plimpton 322 seem to have been computed to provide right-angled triangles covering a range of shapes - their angles actually follow an increasing sequence in roughly equal steps. This raises the question, can the shape of any right-angled triangle be approximated by a Pythagorean triple?"
Show that any right-angled triangle with hypotenuse $1$ may be approximated arbitrarily closely by one with rational sides.
* I also need help on 2nd question in "Constructing rational points" (earboth answered only the "easy" question).