Using the Cotangent

Jim Wilson

Lets use and apply the notation in the figure below. Note we are marking the equivalent segments from each vertex so that the s,  s - a,  s - b, and s - c are in play from the start.    We have three pairs of congruent right triangles so the area is twice the sum of the areas of one from each pair.

A key step in the derivation is the use of the triple cotangent identity when the sum of the three angles is a right angle.