A player’s character is a fixed point in space, not a line or a vector, so is the target. What exactly is the black arrow supposed to represent? Is it supposed to mean the direction the character is moving in? If so, how long is the distance of the green line inside the black line?

I still don’t quite understand how that would help in your example, but getting the angle between two vectors in Roblox can be done with the mathematical definition.

local function angleBetween(v1, v2)
return math.acos(v1:Dot(v2)/(v1.magnitude * v2.magnitude))
end

I don’t know why you use the vocabulary “mathematical definition” when you could just use the word trigonometry. I never knew vector:Dot(vector) existed, I might check documentation.