There are two situations, one is that the angle C is also an acute angle. At this time, two points A and D are taken as the vertical lines of line BC, and the vertical feet are E and F respectively. Exactly BC=BE+EF+CF Because EF=AD=8, the sum of sine value of angle B in right triangle ABE is AB= 15, AE= 15*4/5= 12. According to Pythagorean Theorem, BE=9. In the right triangle CDF, from the known condition CD= 13 and the just found DF=AE= 12, we can get CF=5 according to the pythagorean theorem. Then finally BC=9+8+5=22.

The second case is that the angle c is obtuse. The method is the same as above, except that the vertical foot f is on the extension line of BC, at this time BC = be+ef-cf. Then BC=9+8-5= 12 in this case.