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The problem in the image asks to calculate the distance traveled north and the distance traveled west by a yacht sailing on a bearing of 300° for 65 km. Let me break down how to solve this.

### Step-by-Step Solution:

1. **Understanding the Bearing**:
   - A bearing of 300° is measured clockwise from the north. It is located in the fourth quadrant of the standard Cartesian plane.
   - The angle between the yacht's direction and the north is \( 360^\circ - 300^\circ = 60^\circ \).

2. **Distance Components**:
   - We can break the total distance (65 km) into two components:
     - **Northward Component** (vertical component)
     - **Westward Component** (horizontal component)

3. **Using Trigonometry**:
   - To calculate these components, we use basic trigonometric functions:
     - **Northward (vertical) distance** = \( 65 \times \cos(60^\circ) \)
     - **Westward (horizontal) distance** = \( 65 \times \sin(60^\circ) \)

4. **Calculations**:
   - \( \cos(60^\circ) = 0.5 \)
   - \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \approx 0.866 \)
   
   Now calculating both distances:
   \[
   \text{Northward distance} = 65 \times 0.5 = 32.5 \, \text{km}
   \]
   \[
   \text{Westward distance} = 65 \times 0.866 \approx 56.29 \, \text{km}
   \]

### Final Answer:
- The yacht travels **32.5 km north** and **56.29 km west**.

Would you like more details or have any questions about this process?

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Here are 5 related questions to explore further:
1. What is the bearing for a direction exactly west?
2. How would the problem change if the yacht's bearing was 120°?
3. What would be the distance components if the yacht sailed 100 km on a bearing of 45°?
4. Can the bearing system be applied to a 3D coordinate system?
5. What is the difference between true bearing and magnetic bearing?

**Tip:** Bearings are always measured clockwise from the north and can help with navigation in real-world applications.

By drawing a diagram calculate the distance travelled north and the distance travelled west by a yacht sailing on a bearing of 300° for 65 km (challenge).

Learn how to calculate the distance travelled north and west by a yacht sailing on a bearing of 300° for 65 km using trigonometric functions. This step-by-step solution covers key concepts in trigonometry and vector analysis. Suitable for students in Grades 10-12.

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