The vertical component of the earth's magnetic field is $$6 \times 10^{-5}$$ T at any place where the angle of dip is 37°. The earth's resultant magnetic field at that place will be (Given tan 37° = 3/4)

We have the vertical component of the Earth's magnetic field $$B_V = 6 \times 10^{-5}$$ T and the angle of dip $$\delta = 37°$$, with $$\tan 37° = \frac{3}{4}$$.

The relationship between the vertical component, horizontal component, and the resultant magnetic field is: $$B_V = B \sin \delta$$, where $$B$$ is the resultant (total) magnetic field.

We also know that $$\sin 37° = \frac{3}{5}$$ (since $$\tan 37° = 3/4$$, we have a 3-4-5 triangle giving $$\sin 37° = 3/5$$).

Therefore: $$B = \frac{B_V}{\sin 37°} = \frac{6 \times 10^{-5}}{3/5} = 6 \times 10^{-5} \times \frac{5}{3} = 10 \times 10^{-5} = 1 \times 10^{-4}$$ T.

Hence, the correct answer is Option 4.