It depends on how x and y are defined and if it is a right triangle. For a right triangle the conventional notation would have a right triangle with x being the length of the side adjacent to the 51 degree angle and y being the length of the side opposite the 51 degree angle. The third side would be the hypotenuse with length of 1. With this setup:

x = cos(51) = .629

y = sin(51) = .777

Notice that x^{2} = y^{2} =1

To solve a more general triangle, you need three pieces of information. These can be:

1) two side and the included angle (use law of cosines, then law of sines)

2) two angles and one side (use law of sines)

3) two side and an angle other than the included angle ( much more complicated)