a
Horizontal component of earth's magnetic field, \(B_{H}=0.35 \,G\)

Angle made by the needle with the horizontal plane \(=\) Angle of \(\operatorname{dip}=\delta=22^{\circ}\)

Earth's magnetic field strength \(=B\)

We can relate \(B\) and \(B_{H}\) as: \(B_{H}=B \cos \delta\)

\(\therefore B=\frac{B_{H}}{\cos \delta}\)

\(=\frac{0.35}{\cos 22^{\circ}}=0.377 \,G\)

Hence, the strength of earth's magnetic field at the given location is \(0.377 \;G\)