Absolute Value of Vector with only 2 values and one Angle?

How do I calculate the absolute Value of a Vector when I only know the Values of two Vectors and the angle between them? The Vector I wanna find is the resulting Vector after you add the other 2.

Context: I had Physics today and we were Talking About 2 added Forces(I'm in eigth grade). The teacher said it was not possible for us to calculate the Value of the resulting force and told us to measure it. As I'm counting myself as a mathematician I took that as a challenge and came up with the Formula: cos(|v|/(|v|+|w|)*θ)|w|+cos(|w|/(|v|+|w|)*θ)|v|,Which works if the Ratio between the Angles on either side of a Parallelogramm is the same as the Ratio between the sides(I know it's confusing if you can't see it in front of you) But I have no Idea how to prove it. I just figured that out by measuring the Angles. So my Question is: Is there a better Formula and/or is my "conjecture" About the angle Ratio true or false?

• It can be computed. $\|u+v\|^2=\|u\|^2+\|v\|^2+2(\|u\| \|v\| \cos \theta)$. However you being in eighth grade, I am not sure what things (law of cosines) etc. are you familiar with. – Anurag A Jun 5 at 18:16
• how do you get to that Formula? – kyonite Jun 5 at 18:19
• I already mentioned that in my comment: look up law of cosines. – Anurag A Jun 5 at 18:20
• ooh that one thx – kyonite Jun 5 at 18:24