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The question asks about three forces acting at a point with one of them being 300 N. The angle between the forces is always 40°, and we need to determine the value of \(\theta\) for which the resultant of the three forces is directed parallel to line \(b-b\).

To solve this problem, we will proceed with the following steps:

### Step 1: Understanding the Configuration
- The problem involves three forces with one known force magnitude, 300 N, and the others are likely provided in the figure not visible in the image.
- The angle between the forces is fixed at 40°.

### Step 2: Analyzing the Components
- Let's denote the forces as \(F_1\), \(F_2\), and \(F_3\).
- Assume \(F_1 = 300 \, N\). The directions of \(F_2\) and \(F_3\) will depend on the configuration and the value of \(\theta\).

### Step 3: Using the Resultant Condition
- For the resultant of the three forces to be parallel to \(b-b\), their vector sum must align in a specific direction. This means the sum of the forces' horizontal and vertical components should align in that direction.

### Step 4: Calculating Force Components
- We calculate the horizontal and vertical components of each force based on their angles relative to \(b-b\).
  
If we assume the angle \(\theta\) is the angle one of the forces makes with a reference direction, the components would be:

\[
F_{1x} = 300 \cos \theta, \quad F_{1y} = 300 \sin \theta
\]

Similarly, calculate \(F_2\) and \(F_3\) components assuming their magnitudes are known, and use the fixed angle of 40°.

### Step 5: Setting up Equations for Resultant
- Set up the equations for the resultant's horizontal (\(R_x\)) and vertical (\(R_y\)) components:

\[
R_x = F_{1x} + F_{2x} + F_{3x} = 0 \quad \text{(for parallel to \(y\)-axis)}
\]
\[
R_y = F_{1y} + F_{2y} + F_{3y} \quad \text{(non-zero value)}
\]

### Step 6: Solving for \(\theta\)
- Solve these equations simultaneously to find the value of \(\theta\).

### Conclusion
We need to see the complete diagram or additional information on the other two forces' magnitudes and directions to provide a full numeric solution.

Let me know if you can provide any additional details or would like me to clarify any specific steps further.

**Relative Questions:**
1. What are the magnitudes and directions of the other two forces, if known?
2. Can you confirm the reference direction for the angle \(\theta\) mentioned?
3. Are there any additional constraints or conditions provided in the diagram?
4. Is there a preferred method (vector components or graphical) for solving the force equilibrium?
5. Would you like a general solution template for such problems in different contexts?

**Tip:** Always break forces into components along mutually perpendicular axes when dealing with equilibrium problems. This simplifies the algebra involved in solving the resultant direction and magnitude.

Three forces acting at a point are shown in Fig. The direction of the 300 N forces may vary, but the angle between them is always 40°. Determine the value of θ for which the resultant of the three forces is directed parallel to b-b.

This solution explores how to determine the value of θ for which the resultant of three forces, including a 300 N force, is parallel to b-b. The forces act at a point with an angle of 40° between them, and the solution utilizes vector addition and force component breakdown.

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