Let the vertices of the triangle be #A#, #B#, and #C#.
Theorem:
#color(white)xxa^2+b^2=c^2<=>m(/_C)=90# degrees
#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# degrees
#color(white)xxsin/_A=12/13#
#=>m(/_A)=arcsin(12/13)#
#color(white)xxcolor(white)xxcolor(white)xxcolor(white)x~=67^0 22'37''#
The sum of the measures of the interior angles of a triangle is 180 degrees:
#color(white)xxm(/_A)+m(/_B)+m(/_C)=180# degrees
#=>67^0 22'37''+m(/_B)+90~=180# degrees
#=>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''#
