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The image you've uploaded contains a series of navigational problems that involve calculating courses and distances using given values of *difference in latitude (D'LAT)*, *difference in longitude (D'LONG)*, and *Departure (DMP)*. These types of problems are commonly solved using spherical trigonometry and navigational formulas.

Here's a general breakdown of how to approach the calculations for each set:

1. **Calculate the Course**:
   The course or bearing can be calculated using the formula:
   \[
   \text{Course} = \arctan\left(\frac{\Delta \text{Long}}{\Delta \text{Lat}}\right)
   \]
   The result will be the angle from the North direction (usually in degrees).

2. **Calculate the Distance**:
   The distance is typically calculated based on the *Departure (DMP)*, which is related to the physical distance traveled east or west. You can apply formulas from spherical geometry, depending on the specific navigational method being used (e.g., rhumb line or great circle).

### Example Steps (for a given problem):
1. **Problem 41–42**:
   - Given: \( D'LAT = 22° 00.0' N \), \( DMP = 1624.16 \), \( D'LONG = 020° 30.0' W \)
   - **Calculate Course**:
     Apply the tangent formula for course, using the D'LAT and D'LONG values.
   - **Calculate Distance**:
     You can calculate distance by considering the DMP (departure) value, or apply spherical distance formulas.

Do you want help solving a specific problem from the list, or further clarification on the process?

Here are some related questions to expand your understanding:
1. What is the difference between great circle and rhumb line courses?
2. How does one convert between different units of distance in navigation (e.g., nautical miles)?
3. What role does latitude and longitude play in determining accurate navigation courses?
4. How can you calculate departure (DMP) from given latitude and longitude differences?
5. What are the most common errors to avoid when calculating courses and distances in navigation?

**Tip**: Ensure your calculator is set to degrees when solving for angles, especially for course calculations.

Given D'LAT, D'LONG, and DMP values, calculate the course and distance for the listed problems.

Solve navigational problems by calculating the course and distance using given values of D'LAT (difference in latitude), D'LONG (difference in longitude), and Departure (DMP). Apply spherical trigonometry to calculate the course using arctan(ΔLong / ΔLat) and distance based on DMP.

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