If the angle of dip at places $A$ and $B$ are $30^{\circ}$ and $45^{\circ}$ respectively,the ratio of the horizontal component of the Earth's magnetic field at $A$ to that at $B$ will be.
$[\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}, \quad \sin 30^{\circ}=\frac{1}{2}, \quad \cos 30^{\circ}=\frac{\sqrt{3}}{2}]$

• A
  $\sqrt{2}: 1$
• B
  $1: \sqrt{2}$
• C
  $\sqrt{2}: \sqrt{3}$
• D
  $\sqrt{3}: \sqrt{2}$