# 11.1.3. The Resultant of Coplanar Forces Meeting at a Point

In the figure below, is a regular hexagon, where is the point of intersection of its diagonals, and the forces in the figure are measured in newtons. Find the resultant of the forces and its inclination angle with the positive direction of the -axis, and approximate the result to the nearest minute, if needed.

• AN,
• BN,
• CN,
• DN,

### Example

In the figure below, is a regular hexagon, where is the point of intersection of its diagonals, and the forces in the figure are measured in newtons. Find the resultant of the forces and its inclination angle with the positive direction of the -axis, and approximate the result to the nearest minute, if needed.

### Solution

To find the resultant of a number of coplanar forces acting at a point, we begin by resolving all the forces in the and directions to find the and components of the resultant.

We can see from the figure that the polar angles of the forces (starting with A and moving anticlockwise) are as follows: , , , , , and .

In the direction:

In the direction:

The magnitude of the resultant is given by

The polar angle is given by

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