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The question is asking for the horizontal (\( F_H \)) and vertical (\( F_V \)) components of a force of 9 N at an angle of 32° to the horizontal. To solve this, we can use trigonometric functions:

- The horizontal component (\( F_H \)) is found using \( F_H = F \cdot \cos(\theta) \).
- The vertical component (\( F_V \)) is found using \( F_V = F \cdot \sin(\theta) \).

Where:
- \( F = 9 \, \text{N} \) (the magnitude of the force),
- \( \theta = 32^\circ \) (the angle with the horizontal).

Now, let's compute:

1. \( F_H = 9 \cdot \cos(32^\circ) \)
2. \( F_V = 9 \cdot \sin(32^\circ) \)

Calculating these:

- \( F_H \approx 9 \cdot 0.848 = 7.63 \, \text{N} \) (to 1 decimal place).
- \( F_V \approx 9 \cdot 0.530 = 4.77 \, \text{N} \) (to 1 decimal place).

So:
- \( F_H = 7.6 \, \text{N} \)
- \( F_V = 4.8 \, \text{N} \)

Would you like a detailed breakdown of these calculations?

Here are 5 related questions to explore:

1. How do we calculate components of a force at any angle?
2. What is the relationship between the sine and cosine of complementary angles?
3. How would the force components change if the angle was increased to 45°?
4. Can you derive the resultant force from its components?
5. What are some real-world examples of forces acting at angles?

**Tip**: To avoid errors in trigonometric calculations, ensure that your calculator is set to the correct mode (degrees or radians) based on the angle provided!

Find the horizontal (F_H) and vertical (F_V) components of a force of 9 N at an angle of 32° to the horizontal. Give your answers correct to 1 decimal place.

Learn how to calculate the horizontal and vertical components of a force. This example demonstrates the use of trigonometric functions to decompose a force of 9 N acting at a 32° angle to the horizontal. Ideal for high school students studying physics or trigonometry.

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