A triangle has corners at points A, B, and C. Side AB has a length of #21 #. The distance between the intersection of point A's angle bisector with side BC and point B is #5 #. If side AC has a length of #16 #, what is the length of side BC?
1 Answer
Apr 8, 2016
BC ≈ 8.81
Explanation:
Firstly, let the point where the angle bisector intersects with side 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.
#rArr 5/(DC) = 21/16 # Now cross-multiply :
#21xxDC = 16xx5 # To obtain DC , divide both sides by 21
#rArr (cancel(21) DC)/cancel(21) = (16xx5)/21 #
# rArr DC ≈ 3.81# Now , BC = BD + DC = 5 + 3.81 = 8.81 to 2 decimal places.