The proofing of the triangle is illustrated below.
How to illustrate the proof?
AB = c
BC = a
AC = b
h² = b² - x²
h² = a² - y²
a² - y² = b² - x²
a² = b² - x² + y²
Note that x = c - (c - x) = c
a² = b² - (-x)² + y²
a² = b² + c² + y²
Cos A = x/b
cos = adjacent/hypothenuse
x = bcosA
a² = b² + c² - 2bx
a² = b2 + c² - 2bccosA
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