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. Here is what happens:

We loose most of the significant digits in our result.

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