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The problem asks us to determine the distances traveled north and west by a yacht sailing on a bearing of 300° for 65 km. Let's break this down.

### Step-by-Step Solution:

1. **Understanding Bearing:**
   - A bearing of 300° is measured clockwise from the north. This means the angle is 300° from the north in the clockwise direction.

2. **Finding the Angle with Respect to West:**
   - To find the components of the distance, we need to know the angle with respect to the west direction. Since a full circle is 360°:
   \[
   \text{Angle with respect to west} = 360° - 300° = 60°
   \]
   This is the angle between the direction of travel and the west.

3. **Calculating the Distance Traveled North and West:**
   - We can use trigonometry to find the northward and westward distances:
     - **North Component:** \( \text{Distance} = 65 \times \cos(60°) \)
     - **West Component:** \( \text{Distance} = 65 \times \sin(60°) \)
   - Using values for trigonometric functions:
     - \( \cos(60°) = \frac{1}{2} = 0.5 \)
     - \( \sin(60°) = \frac{\sqrt{3}}{2} \approx 0.866 \)

4. **Calculating the Values:**
   - **North Distance:** \( 65 \times 0.5 = 32.5 \text{ km} \)
   - **West Distance:** \( 65 \times 0.866 = 56.29 \text{ km} \)

### Conclusion:
- **North Distance Traveled:** 32.5 km
- **West Distance Traveled:** 56.29 km

Would you like a more detailed diagram or explanation? Here are 5 related questions you can explore:

1. How do bearings relate to standard angles in trigonometry?
2. What are other real-life applications of bearings?
3. How would the calculation change if the yacht traveled on a bearing of 45°?
4. Can you determine the final position of the yacht using a coordinate system?
5. How would the problem change if the yacht sailed in the opposite direction?

**Tip:** Always draw a diagram for problems involving bearings and angles to visualize the scenario better.

By drawing a diagram, determine the distance travelled north and the distance travelled west by a yacht sailing on a bearing of 300° for 65 km.

Determine the distances traveled north and west by a yacht sailing on a bearing of 300° for 65 km. This problem involves trigonometric concepts, including cosine and sine functions for calculating directional distances. Suitable for students in Grades 9-10.

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