One of the two rectangular components of a force is 10 N and it makes an angle 60° with the force. The magnitude of the force is :

Options

A. 7.1 N
B. 14.1 N
C. 17.3 N
D. 20 N

Explanation

To solve the problem, we need to find the magnitude of the force \( F \) given one of its rectangular components \( F_x = 10 \, \text{N} \) and the angle \( \theta = 60^\circ \) that this component makes with the force.

### Step-by-Step Solution:

1. **Understanding the Components:**
- We have a force \( F \) that can be resolved into two rectangular components: \( F_x \) (the horizontal component) and \( F_y \) (the vertical component).
- The given component \( F_x = 10 \, \text{N} \) makes an angle of \( 60^\circ \) with the force \( F \).

2. **Using the Cosine Relation:**
- The relationship between the force and its component can be expressed using the cosine of the angle:
\[ F_x = F \cdot \cos(\theta) \]
- Here, \( F_x = 10 \, \text{N} \) and \( \theta = 60^\circ \).

3. **Substituting the Values:**
- Substitute the known values into the equation:
\[ 10 = F \cdot \cos(60^\circ) \]

4. **Calculating Cosine of 60 Degrees:**
- We know that \( \cos(60^\circ) = \frac{1}{2} \). Therefore, the equation becomes:
\[ 10 = F \cdot \frac{1}{2} \]

5. **Solving for the Magnitude of the Force \( F \):**
- Rearranging the equation to solve for \( F \):
\[ F = 10 \cdot 2 = 20 \, \text{N} \]

6. **Conclusion:**
- The magnitude of the force \( F \) is \( 20 \, \text{N} \).

### Final Answer:
The magnitude of the force is \( 20 \, \text{N} \).