### Video Transcript

Use the triangle force rule to find
the magnitude of force πΉ 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. Letβs imagine they are drawn
vertically and horizontally as shown. We are trying to find the magnitude
of a third force πΉ 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 πΉ squared. Two squared is equal to four, and
three squared is equal to nine. As the sum of these is 13, we have
πΉ squared equals 13. We can then square root both sides
of this equation. And since the magnitude must be
positive, we have πΉ is equal to root 13. The magnitude of force πΉ is root
13 newtons.