https://r2.erweima.ai/mathbot/image/1726253436874p2im27ua.jpg

The problem in the image involves calculating the components of a force. A 10 N force is applied at an angle of 30° with respect to the vertical axis, and we need to find the horizontal component (\(F_x\)) and the vertical component (\(F_y\)).

### Step-by-step Calculation:
1. **Given:**
   - Force magnitude \( F = 10 \, \text{N} \)
   - Angle \( \theta = 30^\circ \) with the vertical

2. **Finding the components:**
   - \( F_x = F \sin(\theta) \) (since the angle is given with the vertical)
   - \( F_y = F \cos(\theta) \)

3. **Substitute values:**
   - \( F_x = 10 \sin(30^\circ) = 10 \times 0.5 = 5 \, \text{N} \)
   - \( F_y = 10 \cos(30^\circ) = 10 \times \frac{\sqrt{3}}{2} \approx 10 \times 0.866 = 8.66 \, \text{N} \)

So, the components of the force are:
- \( F_x = 5 \, \text{N} \)
- \( F_y = 8.66 \, \text{N} \)

The correct answer is \( F_x = 5 \, \text{N} \) and \( F_y = 8.66 \, \text{N} \), which matches the last option shown in the image.

### Would you like more details on this? Here are some related questions to practice:
1. How would you calculate the force components if the angle were given with the horizontal?
2. What are the horizontal and vertical components if the force is doubled but the angle remains the same?
3. How does the direction of the force affect the signs of \(F_x\) and \(F_y\)?
4. If the angle were 45°, what would the components of the force be?
5. Can you explain how to find the resultant force from its components?

**Tip:** Remember, sine and cosine are based on how the angle is measured relative to the horizontal or vertical. Always check the reference angle when calculating components.

Sobre un cuerpo se aplica una fuerza de 10N y ángulo 30° con la vertical. Calcula Fx, Fy.

Learn how to calculate the horizontal and vertical components of a 10 N force applied at a 30° angle with respect to the vertical. This problem involves key concepts in trigonometry and vector decomposition, suitable for students in Grades 9-11.

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