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The relations amongst the three elements earth's magnetic field, namely horizontal component $\mathrm{H}$, vertical component $\mathrm{V}$ and dip $\delta$ are, $\left(\mathrm{B}_{\mathrm{E}}=\right.$ total magnetic field $)$
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The correct answer is:
$V=B_E \sin \delta, H=B_E \cos \delta$
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
$$
\mathrm{H}=\mathrm{B}_{\mathrm{E}} \cos \delta \text { and } \mathrm{V}=\mathrm{B}_{\mathrm{E}} \sin \delta
$$
Thus, from figure, we can see that
$$
\mathrm{H}=\mathrm{B}_{\mathrm{E}} \cos \delta \text { and } \mathrm{V}=\mathrm{B}_{\mathrm{E}} \sin \delta
$$
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