Triangle Law

Triangle Law

• If two forces are represented in magnitude and direction by two sides of a triangle taken in order, their resultant is represented in magnitude and direction by the third side of the triangle drawn from starting point of first force to end point of the second force.

• While using triangle law to find resultant of two forces, draw one of the two forces from the tip of the other. Then complete the triangle by drawing the third side. The third side drawn from the starting point of first force to the end point of the second force defines the resultant in magnitude and direction. Then use sine and cosine rules.

• Triangle law can be used for composition and resolution of forces along any two directions in the plane.

Solved Examples for Understanding

Example 2. 5. 1 

Find resultant of the two forces shown in Fig. 2.5.1 using triangle law.

Solution:

• Draw line AB parallel to F1 = 20 N and draw line BC parallel to force F2 = 50 N from point B.

• Now, join AC which represents resultant R.

• The two forces are drawn one after the other as shown in Fig. 2.5.1 (a) to form

Δ ABC. As angle made by F1 is 30° with horizontal, its angle with vertical will be 90 – 30 = 60° as shown in the Fig. 2.5.1 (a) at-B.

The angle at C will be

180 - (60 + 20 + 30 + θ = 70 - θ

Example 2.5.2

Find components Fa and Fb of the 100 N force along the directions shown in Fig. 2.5.2 using triangle law.

Solution: 

Example 2.5.3 

If the resultant of the two forces shown in Fig. 2.5.3 is 700 N directed vertically upwards, find the angles α and β using triangle law.

Solution: 

Draw the triangle of forces as shown in Fig. 2.5.3 (a).