MathDB

49

Part of 1976 IMO Longlists

Problems(1)

1976 non similar triangles each with specific angles

Source:

1/30/2011
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}
trigonometrygeometry unsolvedgeometry