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Question: 

A long horizontal wire carries 24.0 A of current due north. What is the net magnetic field 20.0 cm due west of the wire if the Earth’s field there points downward, $44 ^\circ$ below the horizontal, and has magnitude $5.0 \times 10^{-5} \textrm{ T}$?

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer: 

$3.8 \times 10^{-5} \textrm{ T, } 17^\circ \textrm{ below horizontal}$

Giancoli 7th Edition, Chapter 20, Problem 33

(5:17)

Chapter 20, Problem 33 is solved.

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Comments

I find your assigned coordinates very confusing. In the second diagram, how come, the current points to the left when viewed from the side? Also, the said point is 0.2m from the wire but you drew it on the wire. Why?

Never mind, I missed that the wire is horizontal. Thanks