Learn How to Calculate Triangle Law of Forces - Tutorial

Definition:

Triangle law of forces states that, 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.

Example 1 :

Find angle A, C and side c from side a = 5, side b = 6, angle B = 30 using triangle law of forces.^o

Solution:

Let us calculate the value of angle A from angle B.

Step 1:

In the given formula, take sin A on left hand side and multiply a with sin B divided by b which gives, sin A = (a x sin B) / b sin A = (5 x sin 30) / 6 A = sin^-1(0.4167) A = 24.624^o

Step 2:

Angle, A + B + C = π Therefore, C = π - A - B C = 180 - 24.624 - 30 C = 125.376^o

Step 3:

To calculate the value of c: In the given formula, take c on left hand side and multiply a with sin C divided by sin A which gives, c = (a x sin C) / sin A c = (5 x sin 30) / sin 24.624 c = 9.784

Example 2 :

Find angle C, side a, c from side b = 9, angle A = 70^o, angle B = 50^o using triangle law of forces.

Solution:

Let us calculate the value of angle C, side a, side c from angle B.

Step 1:

To calculate the value of angle C: Angle, A + B + C = π C = π - A - B C = 180 - 70 - 50 C = 60^o

Step 2:

To calculate the value of a: In the given formula, take a on the left hand side and multiply b with sin A divided by the sin B which gives, a = (b x sin A) / sin B a = (9 x sin 70) / sin 50 a = 11.04

Step 3:

To calculate the value of c: In the given formula, take c on left hand side and multiply b with sin C divided by sin B which gives, c = (b x sin C) / sin B c = (9 x sin 60) / sin 50 c = 10.175