The vertical component of earth's magnetic field at a place is 3 times the horizontal component. What is the value of angle of dip at this place?

Options

A. `60^(@)`
B. `50^(@)`
C. `30^(@)`
D. `45^(@)`

Explanation

To solve the problem, we need to find the angle of dip (δ) given that the vertical component of Earth's magnetic field (Bv) is 3 times the horizontal component (Bh).

### Step-by-Step Solution:

1. **Identify the relationship between vertical and horizontal components**:
Given that the vertical component (Bv) is 3 times the horizontal component (Bh):
\[ Bv = 3 \cdot Bh \]

2. **Use the formula for the angle of dip**:
The angle of dip (δ) is related to the vertical and horizontal components of the Earth's magnetic field by the formula:
\[ \tan(δ) = \frac{Bv}{Bh} \]

3. **Substitute the value of Bv**:
Substitute the expression for Bv from step 1 into the formula:
\[ \tan(δ) = \frac{3 \cdot Bh}{Bh} \]

4. **Simplify the equation**:
The Bh terms cancel out:
\[ \tan(δ) = 3 \]

5. **Find the angle δ**:
To find the angle of dip, take the arctangent (inverse tangent) of both sides:
\[ δ = \tan^{-1}(3) \]

6. **Calculate δ**:
We know that:
\[ \tan(60^\circ) = \sqrt{3} \approx 1.732 \quad \text{and} \quad \tan(70.5^\circ) \approx 3 \]
Therefore, we can conclude that:
\[ δ \approx 70.5^\circ \]

### Final Answer:
The angle of dip at this place is approximately \( 70.5^\circ \).