1. The problem statement, all variables and given/known data Given that a vector has a magnitude of 6.0 units and makes an angle of 45° and 85° with the x and y axes, respectively, find the x and y components of this vector. Does the given information determine the z component? What can you say about the z component? 2. Relevant equations equations included in #3 below 3. The attempt at a solution What I did was this: solve for x: 6cos45° = 4.24 solve for y: 6cos85° = 5.99 solve for z: sqrt(x^2 + y^2 + z^2) = 6 17.98 + 35.88 + z^2 = 36 z^2 = -17.86 z = ±4.23 Although I got the right answer, I am not 100% sure why. I just tried this to see if it would work and it did. However, I am not sure exactly how the angle on each side is viewed? Is it the angle that the vector projects onto that side of the vector, or is it the angle projected onto the actual axis itself? I'm not sure if I'm even wording that in a way that makes sense, but hoping someone might know of a site or diagram I can look at that shows how the angle is evaluated for each side. I am just a bit confused as to how I get the right answer by multiplying the angle by 6, even though a magnitude of 6 will not necessarily project itself as 6 onto the x axis. I also know something is wrong because when I work backwards to solve for the magnitude of the angle, the value is wrong. I just want to make sure I know how to visualize this properly for related problems.