You can disregard the units for the lengths of the sides of the triangle when you're performing trig calculations such as these. As long as you keep your length units the same for all three sides in the end, you'll be good.

On the note of units for your angle , it depends on how you are calculating it: by hand/mental math? or by calculator?

If it's by a calculator, just make sure that your calculator is set in degrees mode if you're punching in in degrees. Conversely, if you decide to change to radians, make sure your calculator is set in radians mode.