- #1
DanteKennedy
- 32
- 2
- Homework Statement
- Let triangle ABC be a right-angled triangle with angle C = 90°. Let a, b, and c denote the lengths of the sides opposite to vertices A, B, and C, respectively, and let alpha and beta denote the measures of the interior angles at A and B.
- Relevant Equations
- A right triangle is called "critical" if it simultaneously satisfies the following conditions:
1. All side lengths a, b, and c are strictly positive rational numbers
2. The measures of the acute angles alpha and beta, when expressed in pure degrees, are rational numbers (ex. 90°, 68.4°, etc.)
If such a triangle exists, provide an example; if not, prove its non-existence.
No attempts to solve it by myself yet. It would be very nice if someone can help me