A triangle has corners at points A, B, and C. Side AB has a length of #10 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #8 #, what is the length of side BC?
1 Answer
Oct 31, 2017
Explanation:
#"let D be the point on BC where the angle bisector"#
#"intersects BC"#
#"using the "color(blue)"angle bisector theorem"#
#color(red)(bar(ul(|color(white)(2/2)color(black)((AB)/(AC)=(BD)/(DC))color(white)(2/2)|)))larr" find DC"#
#rArr10/8=4/(DC)#
#rArrDC=(4xx8)/10larrcolor(blue)"cross-multiplying"#
#rArrDC=32/10=3 1/5#
#rArrBC=BD+DC=4+3 1/5=7 1/5" units"#
