https://file.aiquickdraw.com/mathbot/file/1725654056253251wkvxv.jpg

The problem presents a cantilever beam subjected to a force \( F = 400 \, \text{N} \) at a 45° angle. To resolve the force into its rectangular components along the \( x \) and \( y \) axes, we need to apply basic trigonometric principles.

1. **Force components**:
   - The horizontal component (along the \( x \)-axis) is given by:
     \[
     F_x = F \cdot \cos(\theta)
     \]
   - The vertical component (along the \( y \)-axis) is given by:
     \[
     F_y = F \cdot \sin(\theta)
     \]
   where \( \theta = 45^\circ \) and \( F = 400 \, \text{N} \).

Let's calculate these components.The force components are:

- \( F_x = 282.84 \, \text{N} \)
- \( F_y = 282.84 \, \text{N} \)

Thus, the correct answer is:
\[
\boxed{F_x = 282.84 \, \text{N}, \, F_y = 282.84 \, \text{N}}
\]
This matches the last option provided in the image.

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

Here are some related questions for further practice:
1. How would the components change if the angle were 30° instead of 45°?
2. What are the force components if the magnitude of \( F \) were 500 N?
3. How do the components behave as the angle approaches 0° or 90°?
4. What is the resultant force when both horizontal and vertical components are known?
5. How would you calculate the moment exerted by the force about the fixed point?

**Tip**: Always use trigonometric functions when resolving forces at angles.

A cantilever beam is subjected to a force F at its free end B. Resolve the force into its rectangular components along the x and y axes. The force F = 400 N is applied at a 45° angle.

Learn how to resolve a 400 N force applied at 45° to a cantilever beam into its rectangular components along the x and y axes. The horizontal and vertical components are calculated using trigonometric principles, providing a clear understanding of force decomposition.

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