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

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

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

$9 / 15 = 8 / DC$

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

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

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