AB = 8 cm, AC = 6 cm, AD = 7 cm, CD = 2.82 and CAB =50°. Find the length BC, angle ABC, angle CAD , area of triangle ACD.

Can't do it.

If you draw A,B,C then D can be anywhere on a circle of radius 2.82 with center at C. There are two places on that circle where AD = 7.