Parallel wires carrying current out of the page, find B

[Dextrine]

Homework Statement

Two parallel wires are a distance 2 b apart from the origin and carry current I out of the plane of the paper.
Find the magnitude and direction of the magnetic field B(y) along the y axis.

Homework Equations

∫B⋅dl=μI[/B]

The Attempt at a Solution

If we take ∫dl = 2πr
B=μI/(2πr)
r=√(b^2+y^2)

Clearly the y components cancel so we are left with only the horizontal components, that is

B_total=2Bcos(θ)

cos(θ)=b/√(b^2+y^2)

However, in the answer key provided, it says that cos(θ)=y/(b^2+y^2)

I don't understand why this would give this horizontal component. It seems like this would give the vertical component.

 

[Dextrine]

Nevermind, I see how. The angle made by the B field from each wire and the horizontal is not the same as the angle between r and b