For this problem we have to use the trig relationships of cos and sin to figure out the lengths. Cos is equal to adjacent/hypotenuse so we can set it as x/r=.814 and since r is equal to 12 we can do 12 times .814 to get x.
We do a similar process for sin but sin is equal to opposite/hypotenuse so we can set up the equation y/r=.581 and we simply multiply both sides by 12 to get 12*.581 to get y.
Also for future reference adjacent and hypotenuse are based on the angle at use, since ∅ is on the bottom left x is the adjacent side and y is the opposite side.
