At a certain location in Africa, a compass points `12^(@)` west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points `60^(@)` above the horizontal. The horizontal component of the earth's field is measured to be 0.16 G. Specify the direction and magnitude of the earth's field at the location.

Explanation

Here declination `theta = 12^(@)` west, dip `theta = 90^(@)`
H = 0.16 gauss `= 0.16 xx 10^(-4)` tesla. R = ?
As `H = R = cos theta`
`R = (H)/(cos theta) = (0.16 xx 10^(-4))/(cos 60^(@))`
`R = (0.16 xx 10^(-4))/(1//2) = 0.32 xx 10^(-4)T`.
The earth's field lies in a vertical plane `12^(@)` west of geographic meridian at an angle of `60^(@)` above the horizontal.