What are the eastern components of the Earth's magnetic field in this city?

[Magna1]

The Earth's magnetic field in this city points towards the north pole and downwards into the ground. The horizontal portion of the Earth's magnetic field is 12.5^10*-6 T and its angle of declination is 22.5 degrees(the angle east of north) What are the eastern components of the Earth's magnetiv field in this city?
I have no idea what to do or where to even start guessing?

 

[Daaf]

So you want to know the vertical component or what? If that is true, you could just use the cosinus or sinus of the angle (22 degrees).

 

[turin]

Originally posted by Magna1
The Earth's magnetic field in this city points towards the north pole and downwards into the ground.

This basically suggests a 3-D coordinate system with y-axis horizontal towards the N-pole, z-axis straight up into the sky, and then the x-axis perpendicular to both of these. All three axes are then mutually perpendicular. Hint #1: Can you imagine in what direction is the x-axis?

In this coordinate system, the magnetic field vector is then:

B = ( B_x , B_y , B_z )
= ( 0 , B_north , -B_upward )

So, the x-component of the magnetic field is zero. In other words, the magnetic field in the x-direction is zero.

EDIT:
I misread the question. I need to change some things in my reply.

Originally posted by Magna1
... its angle of declination is 22.5 degrees(the angle east of north) ...

This seems to contradict the first sentence. I don't know what to tell you. Perhaps the "downward" should be interpreted as if you're in space and looking at the Earth from the orientation that the axis of rotation is vertical and the north pole is on top. I find this a terrible way to word the question, and you have my sympathy. Anyway, this would make the coordinate system 2-D instead of 3-D.

B = ( B_x , B_y )
= ( B sin(22.5^o) , B cos(22.5^o) )

Again, you should decide what you think is the x-direction.

I'm terrible sorry if I have confused you.