c
(c) Horizontal and vertical components of earth's magnetic field are \(B_{h}\) and \(B_{v}\) respectively.

We know that \(B_{h}=B \cos \delta\)

where \(B\) is the earth's total magnetic field and \(\delta\) is the angle of dip.

Also, \(B_{v}=B \sin \delta\)

\(\Longrightarrow B^{2}=B_{h}^{2}+B_{v}^{2}\)

\(\Longrightarrow  B=\sqrt{B_{h}^{2}+B_{v}^{2}}\)