A triangle has corners at 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 #7 #. If side AC has a length of #21 #, what is the length of side BC?

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Answer 1 · 2016-03-17T09:46:41

#BC=16.8#

Let the figure be as follows, in which #AP# bisects angle #A# and cuts #BC# at #P#.

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As #AP# bisects #BC#, according to angle bisector theorem

#(AB)/(AC)=(BP)/(BC)# i.e. here we have

#15/21=7/(CP)# and #CP=21xx7/15=9.8#

Hence, #BC=BP+CP=7+9.8=16.8#.