Define a transcendental angle as a transcendental multiple of a right angle. Are the acute angles of the 3-4-5 right triangle transcendental?
2026-05-04 19:33:40.1777923220
Are the acute angle of a 3-4-5 right triangle transcendental
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$cos(x)=3/4$
The cosine of a rational multiple of a right angle is algebraic.
Per Gelfond-Schneider theorem, the cosine of an irrational, algebraic multiple of a right angle is transcendental.
https://math.stackexchange.com/q/4857678
So $x$ must be a rational or transcendental multiple of a right angle. Per Niven's Theorem, published in Irrational Numbers by Ivan Niven, $x$ can not be a rational multiple of a right angle. So $x$ must be a transcendental multiple of a right angle.