Parallellogram - Euclidean Geometry

Okay I'll just ask the question.

If I know that the sides of a parallellogram is 1 (l.u = length unit ) and 2 l.u and that one angle is 60degrees, can I using plain Euklides Geometry calculate the diagonals exactly?

No need for you guys to solve it completly but a tip would be nice!

I can get all angles easy. This would be a breeze if it was a rectangle, but cuz it's leaning the diagonal must become somewhat longer. I tried to get it by creating it into a 90degree traingle so I could use phytagoras, but for that I'd have to make a million small triangles and I hardly belive it's the easiest way.

Thanks in advance.