Physics help please!?

Question

A long horizontal wire carries 22.0A of current due north. What is the net magnetic field 20.0cm due west of the wire if the Earth's field there points north but downward, 37 degrees below the horizontal, and has magnitude 5.0 x 10^-5 T.

Answer 1

i, j, k unit vectors

At 22 A and 0.2 m west of the wire, the magnetic field has force of
μI/(2πr)=4πE-7*22/(2π*.2)
=22E-6 T our of the paper (k unit vector)

The earth's magnetic field resolved into the y and x directions will be

-5E-5*sin(37) k+5E-5*cos(37) j=-3E-5k+4E-5j

the total filed is
22E-6k-3E-5k+4E-5j
=-0.8E-5k+4E-5j
The magnitude is
sqrt((-0.8E-5)^2+(4E-5)^2)
=4.08E-5 T