# Question Video: Using the Triangle of Forces Rule to find the Magnitude of a Force Mathematics

Use the triangle force rule to Find the magnitude of force πΉ that is in equilibrium with two perpendicular forces of magnitudes 2 and 3 newtons.

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### Video Transcript

Use the triangle force rule to find the magnitude of force πΉ that is in equilibrium with two perpendicular forces of magnitudes two and three newtons.

The triangle force rule states that when three coplanar forces acting at a point are in equilibrium, they can be represented in magnitude and direction by the adjacent sides of a triangle taken in order. In this question, we are told that we have two perpendicular forces of magnitudes two and three newtons. Letβs imagine they are drawn vertically and horizontally as shown. We are trying to find the magnitude of a third force πΉ that maintains equilibrium amongst these three forces. We can do this using the Pythagorean theorem, which states that π squared plus π squared is equal to π squared, where π is the length of the hypotenuse in any right triangle.

Substituting in our values, we have two squared plus three squared is equal to πΉ squared. Two squared is equal to four, and three squared is equal to nine. As the sum of these is 13, we have πΉ squared equals 13. We can then square root both sides of this equation. And since the magnitude must be positive, we have πΉ is equal to root 13. The magnitude of force πΉ is root 13 newtons.