How to solve a triangle with only two sides and the information that there is an angle bisector

Question

One side is 4 cm, the other side is 7.2 cm in total, but the angle bisector divides it into 3.2 cm and 4 cm. 

Answer 1

Use the Angle Bisector/Opposite Side Theorem: A bisector of an angle in a triangle divides the opposite side into two segments whose lengths are in the same ratio as the lengths of the two sides forming the angle.

Draw ΔABC, where AB = 4, BC = 7.2 and AC = the missing side. Let AD be the angle bisector. So, AC=D = 3.2 and CD = 4.

BD/AB = CD/AC

3.2/4 = 4/AC

3.2AC = 16

AC = 5