The x and y components of a vector are ` 4sqrt3 m` and 4 m respectively. What angle does the vector make with positive x-axis ?

Answer

To find the angle that a vector makes with the positive x-axis given its x and y components, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Components**:
- The x-component of the vector is given as \( x = 4\sqrt{3} \, \text{m} \).
- The y-component of the vector is given as \( y = 4 \, \text{m} \).

2. **Use the Tangent Function**:
- The angle \( \beta \) that the vector makes with the positive x-axis can be found using the tangent function:
\[ \tan(\beta) = \frac{y}{x} \]

3. **Substitute the Values**:
- Substitute the values of \( y \) and \( x \) into the equation:
\[ \tan(\beta) = \frac{4}{4\sqrt{3}} \]

4. **Simplify the Expression**:
- Simplifying the right side gives:
\[ \tan(\beta) = \frac{1}{\sqrt{3}} \]

5. **Find the Angle**:
- Now, we need to find the angle \( \beta \) such that:
\[ \tan(\beta) = \frac{1}{\sqrt{3}} \]
- From trigonometric values, we know that:
\[ \beta = 30^\circ \]

### Final Answer:
The angle that the vector makes with the positive x-axis is \( 30^\circ \).

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