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To solve this problem, we will need to compute the reactions at the supports using equilibrium equations based on the forces acting through the cables and rods.

### Step 1: Identify the Forces
The given system involves multiple forces acting on a structure, which includes:
- 20 kN load at point A
- 20 kN load at point C
- 40 kN load at point C (vertical rod)
- 30 kN load at point D

Each cable or rod forms a known angle with the horizontal. The angles provided in the diagram will help in decomposing the forces into horizontal and vertical components.

### Step 2: Apply Equilibrium Conditions
To compute the reactions at the supports, we will apply the following equilibrium equations:
1. **Sum of forces in the horizontal direction (ΣFx = 0)**:
   \[
   \sum F_x = 0
   \]
2. **Sum of forces in the vertical direction (ΣFy = 0)**:
   \[
   \sum F_y = 0
   \]
3. **Sum of moments about a point (ΣM = 0)**:
   \[
   \sum M = 0
   \]

### Step 3: Break Forces into Components
We will decompose each force into its horizontal and vertical components using trigonometry. For example, for a force \( F \) acting at an angle \( \theta \):
- Horizontal component \( F_x = F \cdot \cos(\theta) \)
- Vertical component \( F_y = F \cdot \sin(\theta) \)

#### Cable Forces:
- Force at A (20 kN at 145°): 
  \[
  F_{Ax} = 20 \cdot \cos(145^\circ), \quad F_{Ay} = 20 \cdot \sin(145^\circ)
  \]
- Force at B (20 kN at 90°): 
  \[
  F_{Bx} = 0, \quad F_{By} = 20
  \]
- Force at C (40 kN at 55° and 20 kN vertically):
  - 40 kN: 
    \[
    F_{Cx} = 40 \cdot \cos(55^\circ), \quad F_{Cy} = 40 \cdot \sin(55^\circ)
    \]
  - 20 kN is purely vertical.
- Force at D (30 kN at 115°):
  \[
  F_{Dx} = 30 \cdot \cos(115^\circ), \quad F_{Dy} = 30 \cdot \sin(115^\circ)
  \]
- Cables G and F also contribute to the reactions at points H and I, respectively.

### Step 4: Set Up Equilibrium Equations
- **Horizontal Forces (ΣFx = 0)**:
   We will sum all the horizontal components of the forces and set them equal to zero to solve for the unknown horizontal reactions.

- **Vertical Forces (ΣFy = 0)**:
   Similarly, sum all the vertical forces, including the reaction at points G and I, and set them equal to zero.

- **Moment Equations (ΣM = 0)**:
   Taking moments about a strategic point, such as G or another point, will help eliminate one of the unknown forces and solve for the others.

### Step 5: Solve the System of Equations
Once the equilibrium equations are set, we can solve the system of linear equations to determine the unknown reactions at the supports.

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Would you like me to carry out these calculations step-by-step? I can either proceed with solving the system or clarify any part of the process. Additionally, here are some questions related to this type of problem:

1. How are force components related to their angles in truss or cable systems?
2. What is the significance of choosing a point for taking moments in equilibrium problems?
3. How can we simplify the problem by identifying symmetric loadings or supports?
4. Why is it essential to balance both vertical and horizontal forces in static equilibrium?
5. How does the arrangement of rods and cables affect the reactions at the supports?

**Tip**: When analyzing structures like this, always break forces into components and systematically apply the three equilibrium equations (forces in x, forces in y, and moments).

Compute the reactions of the supports in a system of cables and rods with given loads and angles.

Explore how to calculate the reactions at supports in a structure involving cables and rods under various loads. This guide includes detailed steps using static equilibrium equations, force decomposition, and the application of trigonometry in determining force components. Suitable for university-level engineering students.

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