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,
Triangle center of an isosceles triangle must lie on its line of symmetry. For an equilateral triangle all three components are equal so all centers coincide with the centroid. So, like a circle, an equilateral triangle has a unique center. This is readily seen to be a triangle center function and (provided the triangle is scalene) the corresponding triangle center is the excenter opposite to the largest vertex angle. The other two excenters can be picked out by similar functions. However as indicated above only one of the excenters of an isosceles triangle and none of the excenters of an equilateral triangle