Equilateral triangle 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, so it is also referred to as a regular triangle. Denoting the common length of the sides of the equilateral triangle as "a", we can determine using the Pythagorean theorem that: Denoting the radius of the circumscribed circle as "R", we can determine using trigonometry that: Many of these quantities
Heptagonal triangle heptagonal triangle's orthic triangle, with vertices at the feet of the altitudes, is similar to the heptagonal triangle, with similarity ratio 1:2. The heptagonal triangle is the only obtuse triangle that is similar to its orthic triangle (the equilateral triangle being the only acute one). The various trigonometric identities associated with the heptagonal triangle include these:, The cubic equation has solutions formula_66 and formula_67 which are the squared sines of the angles of the triangle. The positive solution of the cubic equation equals formula_69 which is twice the cosine of one of the triangle’s angles. We also have: For an