The angles of dip at two places are `30^(@)` and `45^(@)` respectively . What is the ratio of horizontal components of earth's magnetic field at the two planes , if vertical components at the two places are same ?

Explanation

To solve the problem, we need to determine the ratio of the horizontal components of the Earth's magnetic field at two locations where the angles of dip are given as \(30^\circ\) and \(45^\circ\). We are also informed that the vertical components of the magnetic field at both locations are the same.

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The angle of dip (or magnetic inclination) at a location is defined as the angle made by the Earth's magnetic field with the horizontal plane. The relationship between the horizontal component (H) and vertical component (V) of the Earth's magnetic field can be expressed using the angle of dip (δ):
\[
\tan(\delta) = \frac{V}{H}
...