A triangle has corners at points A, B, and C. Side AB has a length of #24 #. The distance between the intersection of point A's angle bisector with side BC and point B is #4 #. If side AC has a length of #28 #, what is the length of side BC?

1 Answer
Alberto P.
Oct 26, 2016

#28/24*4=14/3#

Explanation:

Call #alpha=hat A/2#
Use the sin theorem twice on the 2 little triangles identified by bisector (call #beta# and #pi-beta# the angles opposite to #bar(AC# and #bar(AB)# in these triangles and remember that #sin(beta)=sin(pi-beta)#)

#x/sin alpha=28/sin beta#

and

#4/sin alpha=24/sin beta#

substitute and obtain #x=28/24*4=14/3#

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