# Triangle Law of Forces

The resultant of two forces acting at a point can also be found by using Triangle Law of Forces.

If two forces acting at a point are represented in magnitude and direction by the two adjacent sides of a triangle taken in order, then the closing side of the triangle taken in the reversed order represents the resultant of the forces in magnitude and direction.

The triangle law of forces can also be stated as. if a body is in equilibrium under the action of three forces acting at a point, then the three forces can be completely represented by the three sides of a triangle taken in order.

Explanation

Forces P and Q act at an angle 0. In order to find the resultant of P and Q. one can apply the head to tail method, to construct the triangle.

In Figure OA and AB represent P and Q in magnitude and direction. The closing side OB of the triangle taken in the reversed order represents the resultant R of the forces P and Q. The magnitude and the direction of R can be found by using sine and cosine laws of triangles.

If P, Q and R are the three forces acting at a point and they are represented by the three sides of a triangle then, P/OA = Q/AB = R/OB