A triangle has corners at points A, B, and C. Side AB has a length of #9 #. The distance between the intersection of point A's angle bisector with side BC and point B is #8 #. If side AC has a length of #15 #, what is the length of side BC?

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Answer 1 · 2017-12-21T09:16:17

Length of BC = 21.3333

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

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

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

#9 / 15 = 8 / DC#

#DC = (8*15) / (9) = 13.3333#

#BC = BD+DC= 8+13.3333 =21.3333#