A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at `22^@` with the horizontal. The horizontal component of the earth's magnetic field at the place is known to be `0*35G`. Determine the strength of the earth's magnetic field at the place.

Explanation

To solve the problem, we need to determine the strength of the Earth's magnetic field at a given location where the magnetic needle points down at an angle of \(22^\circ\) with the horizontal. We are given the horizontal component of the Earth's magnetic field, \(H = 0.35 \, \text{G}\).

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Angle (\(\theta\)) = \(22^\circ\)
- Horizontal component of the Earth's magnetic field (\(H\)) = \(0.35 \, \text{G}\)

...