Vectors and finding components

[joej24]

Homework Statement

If the x component of a vector A, in the xy plane, is half as large as the magnitude of the vector, the tangent of the angle between the vector and the x-axis is:
A rad 3
B 1/2
C (rad3) / 2
D 3/2
E 3

Homework Equations

The Attempt at a Solution

I first drew a right triangle and realized that the description fit a 30 - 60 - 90 triangle. Is it wrong to assume that the vector and its components make a right triangle?

So I assumed that the magitude of the vector was 2x, the x component x, and the y component (rad 3) x. The tangent of the angle between the angle and x-axis I would then be (rad3)x / x = rad3.
Is this correct? According to my answer sheet, the answer is D (3/2). I don't think the solution sheet is correct

 

[betel]

Y and X axis make a right angle in any reasonable coordinate system. So vector, x and y-axis will make a right triangle.
If rad means square root, then $$\sqrt{3}$$ is the correct answer.

 

[joej24]

Thanks! I think the answer sheet was wrong. And by rad 3 I did mean square root 3.