The relations amongst the three elements earth's magnetic field,...

Let $\mathrm{B}_{\mathrm{E}}$ be the net magnetic field at same point. $\mathrm{H}$ and $\mathrm{V}$ be the horizontal and vertical components of $\mathrm{B}_{\mathrm{E}}$. Let $\delta$ be the angle of dip, which is the angle between direction of earth's magnetic field $B_E$ and horizontal line in the magnetic meridian. Thus, from figure, we can see that $\mathrm{H}=\mathrm{B}_{\mathrm{E}} \cos \delta \text{ and }$\mathrm{V}=\mathrm{B}$_{\mathrm{E}} \sin \delta$