A triangle has corners at points A, B, and C. Side AB has a length of #18 #. The distance between the intersection of point A's angle bisector with side BC and point B is #7 #. If side AC has a length of #14 #, what is the length of side BC?

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Answer 1 · 2017-12-21T11:31:43

Length of side BC = 12.4444

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

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

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

#18 / 14 = 7 / (DC)#

#DC = (7*14) / 18 = 5.4444#

#BC = BD+DC= 7+5.444 =12.4444#