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Learn How to Calculate Triangle Law of Forces - Tutorial

Learn here how to calculate triangle law of forces with neat examples. When there are two forces and if you want to calculate resultant then you can use this law.

How to Calculate Triangle Law of Forces - Definition, Formula and Example

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.

Formula:

a / sin A = b / sin B = c / sin C Where a, b, c = sides of a triangle A, B, C = angles between the sides of a triangle
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 = 24.624o

Step 2:

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

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 = 70o, angle B = 50o 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 = 60o

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