A triangle has corners points A, B, and C. Side AB has a length of #15 #. 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 #18 #, what is the length of side BC?

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Answer 1 · 2017-12-21T09:18:34

Length of BC = 8.8

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

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

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

#15 / 18 = 4 / (DC)#

#DC = (4*18) / 15 = 4.8#

#BC = BD+DC= 4+4.8 =8.8#