Forum Geometricorum, 7 (2007) 25--29.

Abstract: Bailey and Bannister [College Math. Journal, 28 (1997) 182--186] proved that a stronger triangle inequality holds in the Euclidean plane for all triangles having largest angle less than arctan(24/7) (approximately 74 degrees). We use hyperbolic trigonometry to show that a stronger triangle inequality holds in the hyperbolic plane for all triangles having largest angle less than or equal to 65.87 degrees.

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