Given the vector \( R = 53 \, \text{m} \) at an angle of \( 48^\circ \) South of West, you can find the components \( R_x \) (the horizontal component) and \( R_y \) (the vertical component) using trigonometry.

### 1. Understanding the Direction
- The angle \( 48^\circ \) South of West means the angle is measured clockwise from the West direction.

### 2. Calculating the Components
- The horizontal component \( R_x \) is given by:
  \[
  R_x = R \cdot \cos(\theta)
  \]
  Since it's directed Westward, the sign will be negative.
- The vertical component \( R_y \) is given by:
  \[
  R_y = R \cdot \sin(\theta)
  \]
  Since it's directed Southward, the sign will also be negative.

Substituting the values:

\[
R_x = 53 \cdot \cos(48^\circ)
\]
\[
R_y = 53 \cdot \sin(48^\circ)
\]

Now, let's calculate these values:

\[
R_x = 53 \cdot \cos(48^\circ) \approx 53 \cdot 0.6691 \approx 35.46 \, \text{m}
\]
\[
R_y = 53 \cdot \sin(48^\circ) \approx 53 \cdot 0.7431 \approx 39.38 \, \text{m}
\]

### Final Components:
- \( R_x \approx -35.46 \, \text{m} \) (Westward)
- \( R_y \approx -39.38 \, \text{m} \) (Southward)

Would you like more details or have any questions?

### Relative Questions:
1. How would the components change if the vector were 48° North of West?
2. Can you determine the magnitude of \( R \) if only the components \( R_x \) and \( R_y \) are given?
3. What is the physical significance of the negative signs in \( R_x \) and \( R_y \)?
4. How would the components change if the angle were measured from South instead of West?
5. What trigonometric identities are used to derive the horizontal and vertical components of a vector?

**Tip:** Always keep track of the direction when calculating vector components to avoid sign errors.

Learn how to calculate the horizontal and vertical components of a vector given magnitude and angle (53m 48° South of West). Understand trigonometric principles applied to vector analysis. Suitable for Grades 10-12.

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