Integer triangle side of the formula are integers it follows that all integer triangles must have an integer value of "16T" and "T" will be rational. By the law of cosines, every angle of an integer triangle has a rational cosine. If the angles of any triangle form an arithmetic progression then one of its angles must be 60°. For integer triangles the remaining angles must also have rational cosines and a method of generating such triangles is given below. However, apart from the trivial case of an equilateral triangle there are no integer triangles whose angles form either a geometric or
Altitude (triangle) formula_30 we have If is any point on an altitude of any triangle , then For any point within an equilateral triangle, the sum of the perpendiculars to the three sides is equal to the altitude of the triangle. This is Viviani's theorem. In a right triangle the three altitudes , and (the first two of which equal the leg lengths and respectively) are related according to Altitude (triangle) In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite