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You've provided a physics problem where you need to determine the magnitudes of forces \( F_1 \) and \( F_2 \) such that the particle remains in equilibrium, given a force of 12 N acting at an angle of 30° from the x-axis.

For equilibrium, the sum of the forces in both the x-direction and y-direction must be zero. Let's break down the forces into their respective components:

### Components of Forces:
- **12 N force**:
  - \( F_x = 12 \cos(30^\circ) \)
  - \( F_y = 12 \sin(30^\circ) \)

- **

Determine the magnitudes of forces F₁ and F₂ such that the particle remains in equilibrium, given a force of 12 N acting along the x-axis, and F₁ and F₂ acting at angles of 45° and 30° from the horizontal.

Learn how to calculate the magnitudes of forces F₁ and F₂, which are required to keep a particle in equilibrium when a 12 N force acts along the x-axis. This problem explores key concepts like vector decomposition and trigonometry. Suitable for high school physics students.

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