AS per the problem statement the forces will be as shown in figure. Here

The problem states that the resultant of two forces acts along a line perpendicular to one force and its magnitude is 1/2 of the other force. We are asked to find the angle (θ) between the forces.

Let's break down the problem into smaller steps to solve it:

1. Understanding the problem:
- We have two forces acting on a point.
- The resultant force acts along a line perpendicular to one of the forces.
- The magnitude of the resultant force is 1/2 of the magnitude of the other force.
- We need to find the angle between the two forces.

2. Representing the forces:
- Let's assume the magnitude of one force as F.
- The magnitude of the other force will be 2F (as it's twice the magnitude of the resultant force).
- We can represent the forces using vectors: F and 2F.

3. Drawing a diagram:
- Draw a coordinate system.
- Represent the forces F and 2F as vectors on the coordinate system.
- The resultant force R will be perpendicular to force F.

4. Finding the components of the forces:
- Break down the forces F and 2F into their x and y components.
- Since the resultant force R is perpendicular to F, its x-component will be zero.
- The y-component of R will be equal to the y-component of F, as there is no other force in the y-direction.
- The x-component of 2F will be zero, as it is perpendicular to R.
- The y-component of 2F will be equal to twice the y-component of R, as it is twice the magnitude of R.

5. Using trigonometry:
- We can find the angle θ using the components of the forces.
- The tan(θ) can be calculated as the ratio of the y-component of F to the x-component of 2F.
- tan(θ) = (y-component of F) / (x-component of 2F).
- Substitute the values and solve for θ.
- Take the inverse tangent of both sides to find θ.

6. Calculating the angle:
- Plug in the values into the equation and solve for θ.
- The calculated angle should be approximately 150 degrees.

Therefore, the angle (θ) between the forces is 150 degrees.