Solved Example & Practice Problems: Triangle law

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).

Examples for Practice

Q.1

Find resultant of the two forces shown in Fig. 2.5.4 using triangle law.

Q.2

Determine components Fa and Fb of the 500 N force along the directions shown in Fig. 2.5.5 using triangle law.

[ Ans. : Fa = 442.28 N, Fb = 542.53 N]

Q.3

If the resultant of the two forces shown in Fig. 2.5.6 is 90 kN directed vertically upwards, find the angles a and ẞ using triangle law. 

[Ans. : α = 39.29o, β = 56.44°]