Quais são as medidas de ângulo de um triângulo retângulo 5-12-13?

Sejam os vértices do triângulo #A#, #B#e #C#.

Teorema:
#color(white)xxa^2+b^2=c^2<=>m(/_C)=90# graus

#color(white)xxa^2+b^2=5^2+12^2#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x=25+144#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x=169#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x=13^2#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x=c^2#

#=>m(/_C)=90# graus

#color(white)xxsin/_A=12/13#
#=>m(/_A)=arcsin(12/13)#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x~=67^0 22'37''#

A soma das medidas dos ângulos internos de um triângulo é de graus 180:
#color(white)xxm(/_A)+m(/_B)+m(/_C)=180# graus
#=>67^0 22'37''+m(/_B)+90~=180# graus
#=>67^0 22'37''+m(/_B)+90-67^0 22'37''-90~=180-67^0 22'37''-90#
#=>m(/_B)~=90-67^0 22'37''#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x=22^0 37'53''#