Equilateral triangle a triangle with any two sides "a" and "b", and an angle "C" between them is Each angle of an equilateral triangle is 60°, so The sine of 60° is formula_50. Thus since all sides of an equilateral triangle are equal. Equilateral triangles have frequently appeared in man made constructions: Equilateral triangle In geometry, an equilateral triangle is a triangle in which all three sides are equal. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon,
Equilateral triangle root formula_33 of 1 the triangle is equilateral if and only if Given a point "P" in the interior of an equilateral triangle, the ratio of the sum of its distances from the vertices to the sum of its distances from the sides is greater than or equal to 2, equality holding when "P" is the centroid. In no other triangle is there a point for which this ratio is as small as 2. This is the Erdős–Mordell inequality; a stronger variant of it is Barrow's inequality, which replaces the perpendicular distances to the sides with the distances from "P"