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.