Parallelogram lengths

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Hello. i've been really bored and have taken to drawing with my old stencil, and doing some geometry. I was just thinking about what the ratio of the two long sides of the parallelogram was. The parallelogram has sides a, b, and c (pictured below), which helped me solve for more parts of the parallelogram. I labeled the two long sides x and y, and i was able to create a formula for x using the pythagorean theorem, which was [https://imgur.com/a/IQbrRHW]. Upon further testing, I found that it instead works for y. I also created a formula for y using the rule of cosines, which is [https://imgur.com/a/ozO2X3R]. Again, this one works for x when i tested with the actual lengths. What i'm asking is first of all if the formulas are correct and why the formulas i made worked for the opposite ones. Maybe I just mixed up my notes, but eh. Also, if there are other ways to get these answers or what the correct answers are if my ones are incorrect. The actual angles of the parallelogram are 60 and 120. The real lengths of a, b, and c are about 2.4, 1,6, and 0.8 respectively. Good luck. Also, x is the shorter one. Y is the longer one.