Enola's First Theorem?

Factual Questions
1

A few years ago I found something odd about right triangles and trig functions:

Any right triangle with unit degrees (not decimals nor fractions…e.g. a 30-60-90 deg triangle) won’t have legs or a hypotenuse with all non-decimal or -fractional units of length.

Conversely, a perfect pythagorean triangle, e.g. 3-4-5 or 5-12-13 won’t have non-decimal or -fractional degrees.

(Don’t ask for better examples…I’ve lost my trig books and my scientific calcualtor is dead.)

Has a mathematician discovered this mutual exclusion complimentarity before?

2

Yes. Basically, rational angles have transcendental sines, cosines and tangents and, conversely, an angle with a rational (or even non-transcendental) values of the trig functions will have transcendental angle measure.