Let's solve the problem to determine the reactions at points A and B.

### Given Data:
- Force \( F_1 = 10,000 \) lb (acting vertically downward).
- Force \( F_2 = 24,000 \) lb (acting at a 60° angle to the horizontal).
- Distance \( AB = 24 \) inches.
- Angle \( \theta = 20° \).

### Steps for Solution:

#### 1. **Resolve the Force \( F_2 \) into Components:**
   - The horizontal component of \( F_2 \):
     \[
     F_{2x} = F_2 \cos(60°)
     \]
   - The vertical component of \( F_2 \):
     \[
     F_{2y} = F_2 \sin(60°)
     \]

   Given \( F_2 = 24,000 \) lb:
   \[
   F_{2x} = 24,000 \times \cos(60°) = 24,000 \times 0.5 = 12,000 \text{ lb}
   \]
   \[
   F_{2y} = 24,000 \times \sin(60°) = 24,000 \times \frac{\sqrt{3}}{2} \approx 20,784 \text{ lb}
   \]

#### 2. **Equilibrium Equations:**
Since the system is in equilibrium, we can apply the following conditions:

- **Horizontal Forces (\(\sum F_x = 0\)):**
  \[
  A_x + B_x - F_{2x} = 0
  \]
  \[
  A_x + B_x = 12,000 \text{ lb}
  \]

- **Vertical Forces (\(\sum F_y = 0\)):**
  \[
  A_y + B_y - F_1 - F_{2y} = 0
  \]
  \[
  A_y + B_y = 10,000 \text{ lb} + 20,784 \text{ lb} \approx 30,784 \text{ lb}
  \]

- **Moments about Point A (\(\sum M_A = 0\)):**
   Taking moments about point A (assuming clockwise moments are positive):
   \[
   - B_y \times 24 + 10,000 \times 24 + 20,784 \times 24 \cos(20°) = 0
   \]

   Simplifying:
   \[
   B_y \times 24 = 30,784 \times 24 \times \cos(20°)
   \]
   \[
   B_y = 30,784 \times \cos(20°) \approx 28,938.7 \text{ lb}
   \]

   Substituting \( B_y \) into the vertical force equilibrium equation:
   \[
   A_y + 28,938.7 = 30,784 \text{ lb}
   \]
   \[
   A_y = 30,784 - 28,938.7 \approx 1,845.3 \text{ lb}
   \]

#### 3. **Determine \( B_x \) and \( A_x \):**
   - From the horizontal equilibrium equation:
     \[
     A_x + B_x = 12,000 \text{ lb}
     \]

   Assuming \( B_x = 0 \) (no horizontal reaction at B due to symmetry or design considerations):
   \[
   A_x = 12,000 \text{ lb}
   \]

### Final Reactions:
- \( A_x = 12,000 \) lb (horizontal reaction at A)
- \( A_y \approx 1,845.3 \) lb (vertical reaction at A)
- \( B_y \approx 28,938.7 \) lb (vertical reaction at B)

Would you like to dive into the specifics of these calculations or explore how these reactions impact the design or safety of the landing gear?

### Follow-Up Questions:
1. Would you like to verify the moment calculations for another point?
2. Should we analyze the effect of changing angles on the reaction forces?
3. Do you need to consider friction or other forces acting on the landing gear?
4. Would you like to discuss how these reaction forces are used in structural analysis?
5. Are there additional components or forces you'd like to include in the analysis?

### Tip:
When solving for reactions, always check the direction and magnitude of each force component to ensure consistency with the physical setup of the problem.

Learn how to determine reactions at points A and B in statics problems with a detailed step-by-step solution. This problem involves resolving forces, applying equilibrium equations, and calculating moments. Suitable for advanced engineering students and professionals.

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