At a certain place, the horizontal component of earth's magnetic field is $\frac{1}{\sqrt{3}}$ times the vertical component. The angle of dip at that place is

Recall the formula of the angle of dip in terms of vertical component and horizontal component,

Angle of dip is defined as the ratio of vertical component of magnetic field to horizontal component of magnetic field.

$$\begin{gathered} \tan \theta =\frac{B_V}{B_H}=\frac{B_V}{{\displaystyle \frac{1}{\sqrt{3}}}{B}_V}=\sqrt{3} \\ \Rightarrow \theta =60° \end{gathered}$$