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The problem asks to find the resultant force of two forces, \( F_1 = 200 \, \text{N} \) and \( F_2 = 200 \, \text{N} \), where \( F_1 \) is horizontal along the x-axis, and \( F_2 \) is at an angle of \( 60^\circ \) to the x-axis, as shown in the image.

### Solution:
To find the resultant force \( F_R \), we need to break down the forces into their components and use vector addition:

1. **Components of \( F_1 \):**
   Since \( F_1 \) is entirely along the x-axis:
   \[
   F_{1x} = 200 \, \text{N}, \quad F_{1y} = 0 \, \text{N}
   \]

2. **Components of \( F_2 \):**
   The force \( F_2 \) makes an angle of \( 60^\circ \) with the x-axis. Using trigonometry:
   \[
   F_{2x} = F_2 \cos(60^\circ) = 200 \cos(60^\circ) = 200 \times 0.5 = 100 \, \text{N}
   \]
   \[
   F_{2y} = F_2 \sin(60^\circ) = 200 \sin(60^\circ) = 200 \times \frac{\sqrt{3}}{2} \approx 200 \times 0.866 = 173.2 \, \text{N}
   \]

3. **Resultant force components:**
   Now, we can sum the x and y components:
   \[
   F_{Rx} = F_{1x} + F_{2x} = 200 + 100 = 300 \, \text{N}
   \]
   \[
   F_{Ry} = F_{1y} + F_{2y} = 0 + 173.2 = 173.2 \, \text{N}
   \]

4. **Magnitude of the resultant force:**
   The magnitude of the resultant force \( F_R \) is found using the Pythagorean theorem:
   \[
   F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} = \sqrt{300^2 + 173.2^2} = \sqrt{90000 + 30001.44} = \sqrt{120001.44} \approx 346.4 \, \text{N}
   \]

So, the resultant force is approximately **346.4 N**, which matches the last option in the list.

### Final Answer: 
\[
F_R \approx 346.4 \, \text{N}
\]

Would you like more details on any of the steps, or do you have any questions?

### Related Questions:
1. How do you resolve forces into their components?
2. Why do we use the Pythagorean theorem to find the magnitude of the resultant?
3. What is the significance of the angle in force decomposition?
4. How would the resultant force change if \( F_2 \) had a different angle?
5. How do we calculate the direction of the resultant force?

### Tip:
Always decompose forces into their x and y components to simplify vector addition. This method works universally for any vector problem.

Find out the Resultant Force. Given: F1 = 200 N along the x-axis, F2 = 200 N at an angle of 60° to the x-axis.

Learn how to calculate the resultant force of two vectors with detailed step-by-step solutions. This problem uses vector addition, trigonometry, and the Pythagorean Theorem. Suitable for students in Grades 10-12.

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