At a place horizontal and vertical components of `B_H= 3^(1/2)G`, `5^0`West of North. `B_v=1 G` vetically upward. Then angle of inclination and declination are respectively earth's magnetic field are as follows

Options

A. `60^0`, `5^0` W
B. `30`,`5^0` W
C. `30^0`, `5^0` E
D. `60^0`, `5^0` E

Answer

To solve the problem, we need to determine the angle of inclination and declination of the Earth's magnetic field based on the given horizontal and vertical components of the magnetic field.

### Given:
- Horizontal component of the magnetic field, \( B_H = 3^{1/2} \, \text{G} \) at an angle of \( 5^\circ \) West of North.
- Vertical component of the magnetic field, \( B_V = 1 \, \text{G} \) vertically upward.

### Step 1: Understanding the Components
The horizontal component \( B_H \) is directed at \( 5^\circ \) West of North. This means that the magnetic field is tilted towards the west from the north direction.

### Step 2: Calculate the Angle of Inclination
The angle of inclination \( \theta \) can be calculated using the formula:
\[ \tan(\theta) = \frac{B_V}{B_H} \]
Substituting the values:
\[ \tan(\theta) = \frac{1 \, \text{G}}{3^{1/2} \, \text{G}} = \frac{1}{\sqrt{3}} \]
From trigonometric values, we know that:
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]
Thus, we find:
\[ \theta = 30^\circ \]

### Step 3: Determine the Angle of Declination
The declination angle \( D \) is the angle between the magnetic meridian and the geographic meridian. Since the horizontal component is directed \( 5^\circ \) West of North, the declination angle is:
\[ D = 5^\circ \, \text{West} \]

### Conclusion
The angles of inclination and declination are:
- Angle of Inclination \( \theta = 30^\circ \)
- Angle of Declination \( D = 5^\circ \, \text{West} \)

### Final Answer
The angle of inclination and declination are respectively \( 30^\circ \) and \( 5^\circ \, \text{West} \).

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