A triangle has corners at points A, B, and C. Side AB has a length of #48 #. The distance between the intersection of point A's angle bisector with side BC and point B is #9 #. If side AC has a length of #45 #, what is the length of side BC?

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Answer 1 · 2017-12-21T11:33:55

Length of side BC = 17.4375

Let the point where the angle bisector intersects with
side BC be D

#"using the "color(blue)"angle bisector theorem"#

#(AB)/(AC)=(BD)/(DC)#

#48 / 45 = 9 / (DC)#

#DC = (9*45) / 48 = 8.4375#

#BC = BD+DC= 9+8.4375 =17.4375#