A triangle has corners at points A, B, and C. Side AB has a length of #38 #. 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 #44 #, what is the length of side BC?

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Answer 1 · 2017-01-07T10:26:31

#BC=328/19~=17.26#

Let AD be the point A's bisector (D is the intersection of bisector with side BC.

By the bisector theorem there is a relation between the sides of the triangle and the parts of the side cut by the bisector:

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

The known sides are AB=38 and AC=44 and the part of side BC, BD=8. Then you can find DC:

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

#DC=(cancel8^4*44)/cancel38^19=176/19~=9.26#

Then #BC=BD+DC=8+176/19=328/19~=17.26#