2014-12 Rational ratios in a triangle

Determine all triangles ABC such that all of \( \frac{AB}{BC}, \frac{BC}{CA}, \frac{CA}{AB}, \frac{\angle A}{\angle B}, \frac{\angle B}{\angle C}, \frac{\angle C}{\angle A}\) are rational.

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2014-12 Rational ratios in a triangle, 2.7 out of 5 based on 7 ratings