The problem states that eleven forces, each equal to 5n, act on a particle simultaneously. Each force makes an angle of 30 degrees with the next one. We need to find the resultant of all these forces.

To solve this problem, we can use vector addition. Since all the forces act on the same particle, we can add them together to find the resultant force.

Step 1: Resolving the forces
Since the forces are at an angle of 30 degrees with each other, we can resolve each force into its horizontal and vertical components using trigonometry.

Let's consider the first force, F1. The horizontal component of F1 can be found using the formula: F1x = F1 * cos(30°). Similarly, the vertical component of F1 can be found using the formula: F1y = F1 * sin(30°).

We can repeat this process for all the forces, resulting in a total of eleven horizontal components (F1x, F2x, F3x, ..., F11x) and eleven vertical components (F1y, F2y, F3y, ..., F11y).

Step 2: Adding the horizontal and vertical components
Now that we have the horizontal and vertical components of each force, we can add them separately to find the total horizontal and vertical components.

The total horizontal component (Rx) is the sum of all the horizontal components: Rx = F1x + F2x + F3x + ... + F11x.

Similarly, the total vertical component (Ry) is the sum of all the vertical components: Ry = F1y + F2y + F3y + ... + F11y.

Step 3: Finding the resultant force
Using the total horizontal (Rx) and vertical (Ry) components, we can find the magnitude and direction of the resultant force.

The magnitude of the resultant force (R) can be found using the Pythagorean theorem: R = √(Rx^2 + Ry^2).

The direction of the resultant force (θ) can be found using the inverse tangent function: θ = tan^(-1)(Ry / Rx).

Conclusion
By following these steps, we can find the resultant of all the forces acting on the particle. Remember to use the given values (11 forces each equal to 5n and an angle of 30 degrees between each force) in the calculations to obtain the final numerical answer.