The true dip at a place is `30^(@)` . What is the apparent dip when the dip circle is turned `60^(@)` out of the magnetic meridian ?

Answer

To solve the problem of finding the apparent dip when the dip circle is turned 60 degrees out of the magnetic meridian, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- True dip (ρ) = 30 degrees
- Angle turned out of the magnetic meridian (θ) = 60 degrees

2. **Use the Formula for Apparent Dip**:
The relationship between the true dip and the apparent dip when the dip circle is turned is given by the formula:
\[ \tan(\delta') = \frac{\tan(\rho)}{\cos(\theta)} \]
where:
- δ' = apparent dip
- ρ = true dip
- θ = angle turned out of the magnetic meridian

3. **Calculate the Tangent of the True Dip**:
We need to find \(\tan(30^\circ)\):
\[ \tan(30^\circ) = \frac{1}{\sqrt{3}} \]

4. **Calculate the Cosine of the Angle Turned**:
Next, we need to find \(\cos(60^\circ)\):
\[ \cos(60^\circ) = \frac{1}{2} \]

5. **Substitute Values into the Formula**:
Now, substitute the values into the formula:
\[ \tan(\delta') = \frac{\tan(30^\circ)}{\cos(60^\circ)} = \frac{\frac{1}{\sqrt{3}}}{\frac{1}{2}} = \frac{2}{\sqrt{3}} \]

6. **Calculate the Apparent Dip**:
To find the angle δ', we take the arctangent:
\[ \delta' = \tan^{-1}\left(\frac{2}{\sqrt{3}}\right) \]

7. **Approximate the Value**:
Using a calculator or trigonometric tables:
\[ \delta' \approx 49.7^\circ \]

### Final Answer:
The apparent dip when the dip circle is turned 60 degrees out of the magnetic meridian is approximately **49.7 degrees**.