ABCD is a parallelogram and this figure is NOT drawn to scale.

The angle does not matter. Think of it as finding the other side to a triangle. Use [tex]a ^{2} +b^2 =c^2 [/tex]

a=39 (line AB)
b=b (the leg we need to find)
c=89 (line BD)

[tex]39^2 + b^2 = 89^2 [/tex]
[tex]1521 + b^2 = 7921 [/tex]
(subtract the 1521 from both sides)
[tex]b^2 = 6400[/tex]
(square root both sides)
[tex] \sqrt{(b^2)} = \sqrt{6400} [/tex]

b = 80
AD=80