Problem

Problem

Consider the following statements concerning in ΔABC\Delta ABC. Prove that (i) ⇒\Rightarrow (ii) ⇒\Rightarrow (iii) ⇒\Rightarrow (i). (i) The sides a,b,ca, b, c and area Δ\Delta are rational. (ii) a,tan⁡B2,tan⁡C2a, \tan \frac{B}{2}, \tan \frac{C}{2} are rational. (iii) a,sin⁡A,sin⁡B,sin⁡Ca, \sin A, \sin B, \sin C are rational.

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