A ship sailed 6 km due south from the harbour and then 7 km due east, reaching its destination, Draw a diagram,what is the compass bearing of the ship at its destination?

To solve this problem, we can start by visualizing the path of the ship with a diagram. The ship's journey forms a right-angled triangle, where the ship first travels 6 km south and then 7 km east. 

Here's a step-by-step process to determine the compass bearing:

1. **Diagram Drawing:**
   - Draw a vertical line downwards (representing south) for 6 km from the origin (harbour).
   - From the end of this line, draw a horizontal line to the right (representing east) for 7 km.

2. **Right Triangle Analysis:**
   - The origin (harbour) is at point \( H \).
   - The end of the southward path is at point \( A \).
   - The final destination is at point \( B \).

   The right-angled triangle \( HAB \) has:
   - \( HA = 6 \) km (south)
   - \( AB = 7 \) km (east)

3. **Finding the Compass Bearing:**
   - The compass bearing is measured from the north in a clockwise direction.
   - First, find the angle θ between the line \( HA \) (south direction) and the line \( HB \) (the hypotenuse).

   We use trigonometry (specifically the tangent function):
   \[
   \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} = \frac{7}{6}
   \]
   \[
   \theta = \tan^{-1}\left(\frac{7}{6}\right)
   \]
   Calculate θ:
   \[
   \theta \approx 49^\circ
   \]

4. **Compass Bearing:**
   - Since the ship travels south first and then east, the bearing will be from the south towards the east.
   - Compass bearing from the north is \( 180^\circ + 49^\circ = 229^\circ \).

   Thus, the compass bearing of the ship at its destination is approximately \( 229^\circ \).

### Diagram

Here's a representation of the ship's journey:

```
Harbour (H)
     |
     | 6 km South
     |
     A------- 7 km East
            |
            B (Destination)
```

### Solution:

The compass bearing of the ship at its destination is approximately \( 229^\circ \).

Would you like more details on any part of this solution, or do you have any questions?

### Related Questions:

1. How do you convert a bearing from degrees to radians?
2. What is the distance from the harbour to the destination in a straight line?
3. How do you calculate the bearing if the ship travelled 6 km north and 7 km west?
4. What are the components of a vector in navigation problems?
5. How do you determine the angle between two vectors?
6. Can you explain the difference between true bearing and magnetic bearing?
7. How would the bearing change if the ship travelled 6 km south and then 7 km west?
8. How do bearings affect navigation and route planning?

### Tip:

When working with bearings, always remember that they are measured clockwise from the north direction. This standardizes the measurement across different navigational problems.

Learn how to calculate the compass bearing of a ship that travels 6 km due south and then 7 km due east. This problem involves trigonometric concepts, including the tangent function, and is suitable for students in Grades 7-9.

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