Lei dos cossenos

a^2=h^2+〖(c-m)〗^2

 h^2=b^2-m^2

substituindo

a^2=b^2-m^2+[(c-m)〗^2
a^2=b^2+c^2-2c.m

ACH  é  retângulo

CosÂ=b/m
m=b/cosÂ

 a^2=b^2+c^2-2b.c.cos Â

ABC  é  obtusângulo 

a^2=h^2+〖(b+m)〗^2
 c^2=h^2+m^2
h^2=c^2 -m^2


substituindo

a^2=c^2-m^2+〖(b+m)〗^2
a^2=c^2+b^2+2bm

cos(180º-Â)=-cosÂ=m/c
m=-c.cosÂ

a^2=b^2+c^2-2b.c.cosÂ

Lei  dos  cossenos