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1976 non similar triangles each with specific angles

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January 30, 2011
trigonometrygeometry unsolvedgeometry

Problem Statement

Determine whether there exist 19761976 nonsimilar triangles with angles α,β,γ,\alpha, \beta, \gamma, each of them satisfying the relations sin⁡α+sin⁡β+sin⁡γcos⁡α+cos⁡β+cos⁡γ=127 and sin⁡αsin⁡βsin⁡γ=1225\frac{\sin \alpha + \sin\beta + \sin\gamma}{\cos \alpha + \cos \beta + \cos \gamma}=\frac{12}{7}\text{ and }\sin \alpha \sin \beta \sin \gamma =\frac{12}{25}
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