A triangle has corners at points A, B, and C. Side AB has a length of #44 #. The distance between the intersection of point A's angle bisector with side BC and point B is #16 #. If side AC has a length of #32 #, what is the length of side BC?
1 Answer
Apr 19, 2016
≈ 27.64
Explanation:
The first step is to let the point where the angle bisector intersects with BC be D.
Then by the
#color(blue)" Angle bisector theorem " #
# (BD)/(DC) = (AB)/(AC) # Require to find DC.
Substitute the appropriate values into the ratio to obtain.
# 16/(DC) = 44/32 # Now cross-multiply
#rArr 44xxDC = 32xx16 # now divide both sides by 44
# (cancel(44) DC)/cancel(44) = (32xx16)/44 #
#rArr DC ≈ 11.64 # and BC = BD + DC = 16 + 11-64 = 27.64
