A man walk 20 m at an angle` 60^(@)` north of east . How far towards east has he he travellled ?

Options

A. 10 m
B. 20 m
C. `20sqrt(3)` m
D. `10sqrt(3)`m

Explanation

To solve the problem of how far the man has traveled towards the east after walking 20 meters at an angle of 60 degrees north of east, we can break down the movement into its components using trigonometry.

### Step-by-Step Solution:

1. **Understand the Vector Components**:
- The man walks at an angle of 60 degrees north of east. This means that we can break his movement into two components: one towards the east and one towards the north.

2. **Identify the Magnitude of the Vector**:
- The total distance walked by the man is given as 20 meters. This is the magnitude of the vector.

3. **Determine the Eastward Component**:
- To find out how far he has traveled towards the east, we need to calculate the eastward component of the vector. This can be done using the cosine of the angle.
- The formula for the eastward component (A_E) is:
\[ A_E = A \cdot \cos(\theta) \]
- Where:
- \( A \) is the magnitude of the vector (20 meters).
- \( \theta \) is the angle (60 degrees).

4. **Calculate the Cosine of the Angle**:
- We know that:
\[ \cos(60^\circ) = \frac{1}{2} \]

5. **Plug in the Values**:
- Now we can substitute the values into the formula:
\[ A_E = 20 \cdot \cos(60^\circ) = 20 \cdot \frac{1}{2} = 10 \text{ meters} \]

6. **Conclusion**:
- Therefore, the man has traveled **10 meters towards the east**.

### Final Answer:
The distance traveled towards the east is **10 meters**.

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