To find the horizontal ($F_H$) and vertical ($F_V$) components of the forces, we use trigonometry. The general formulas are:

• $F_H = F \cos(\theta)$
• $F_V = F \sin(\theta)$

Where:

• $F$ is the magnitude of the force,
• $\theta$ is the angle the force makes with the horizontal axis.

For the first force (12 N at 35°):

• Horizontal component:
  $F_H = 12 \cos(35^\circ)$ $F_H \approx 12 \times 0.8192 \approx 9.8 \, \text{N}$

• Vertical component:
  $F_V = 12 \sin(35^\circ)$ $F_V \approx 12 \times 0.5736 \approx 6.9 \, \text{N}$

For the second force (7 N at 73°):

• Horizontal component:
  $F_H = 7 \cos(73^\circ)$ $F_H \approx 7 \times 0.2924 \approx 2.0 \, \text{N}$

• Vertical component:
  $F_V = 7 \sin(73^\circ)$ $F_V \approx 7 \times 0.9563 \approx 6.7 \, \text{N}$

Final Answers:

1. For the 12 N force:

   • $F_H \approx 9.8 \, \text{N}$
   • $F_V \approx 6.9 \, \text{N}$

2. For the 7 N force:

   • $F_H \approx 2.0 \, \text{N}$
   • $F_V \approx 6.7 \, \text{N}$

Would you like further details or any clarification?

Here are some related questions:

1. How do we calculate the resultant force from its components?
2. What happens to the force components if the angle increases?
3. Can you explain the concept of vector decomposition in detail?
4. How can we calculate the angle of a force given its components?
5. What are the applications of resolving forces into components in engineering?

Tip: Remember, the horizontal component is always associated with cosine, and the vertical component is with sine when resolving forces at an angle.