Computers represent floating-point number internally in a format similar to scientific notation. The very worse thing that you can do with numbers represented in scientific notation is subtract numbers of similar magnitude. We loose most of the significant digits in our result (see next slide).

In the case of triangles, these sort of precision problems to occur frequently, because in general the vertices of a triangle are close to each other.

and thus

Thankfully, we can avoid this subtraction of large numbers when computing an expression for C. Given that we know A and B we can solve for C as follows:

or

To eliminate any bias toward either vertex we will average of these C values