Three concurrent force of the same magnitude are in equilibrium. What is the angle between the forces? Also name the triangle formed by the forces as sides.

Options

A. `60^(@)` equilateral triangle
B. `120^(@)`, equilateral triangle
C. `30^(@)`, an isosceles triangle
D. `120^(@)`, an obtuse angled triangle

Explanation

To solve the problem of finding the angle between three concurrent forces of the same magnitude that are in equilibrium, we can follow these steps:

### Step 1: Understand the Concept of Equilibrium
Three forces are said to be in equilibrium when the net force acting on a point is zero. This means that the vector sum of the three forces must cancel each other out.

**Hint:** Remember that for forces to be in equilibrium, they must balance each other out.

### Step 2: Identify the Forces
Let’s denote the three forces as \( F_1 \), \( F_2 \), and \( F_3 \). Since they are of the same magnitude and are concurrent, they can be represented as vectors originating from a common point.

**Hint:** Visualize the forces as arrows starting from the same point.

### Step 3: Determine the Angles Between the Forces
Since the magnitudes of the forces are equal, the angles between them must also be equal for the forces to be in equilibrium. Let’s denote the angle between any two forces as \( \theta \).

**Hint:** If the forces are equal in magnitude and in equilibrium, the angles must be symmetrical.

### Step 4: Use the Properties of a Triangle
The three forces can be represented as the sides of a triangle. The sum of the angles in a triangle is always \( 180^\circ \). Since there are three equal angles in this triangle, we can express this as:
\[ 3\theta = 180^\circ \]
From this, we can solve for \( \theta \):
\[ \theta = \frac{180^\circ}{3} = 60^\circ \]

**Hint:** Remember that the angles in a triangle sum up to \( 180^\circ \).

### Step 5: Identify the Type of Triangle Formed
Since all three sides (forces) are equal in magnitude and all angles are equal, the triangle formed is an equilateral triangle.

**Hint:** An equilateral triangle has all sides and angles equal.

### Conclusion
The angle between the three concurrent forces of the same magnitude that are in equilibrium is \( 60^\circ \), and the triangle formed by these forces is an equilateral triangle.

### Final Answer
- **Angle between the forces:** \( 60^\circ \)
- **Type of triangle formed:** Equilateral triangle