Explanation

(b) Angle of dip is defined as the angle at a particular point on the earth’s surface between the direction of the earth’s magnetic field and
$B_{H} = B\cos\delta$
Where $B$ is total field intensity, $B_{H}$ the horizontal component of earth’s magnetifc field and $\theta$ the dip angle.
Given, $\delta = 30{^\circ}$
$\because\ \cos{30{^\circ} = \frac{\sqrt{3}}{2}}$
$\therefore B = \frac{B_{H}}{\cos{30{^\circ}}} = \frac{2B_{H}}{\sqrt{3}\ }$