### Video Transcript

Three coplanar forces π
sub
one, π
sub two, and π
sub three are acting on a body in equilibrium. The triangle of forces forms a
right triangle as shown. Given that the magnitude of π
sub one equals five newtons and the magnitude of π
sub two equals 13 newtons,
find the magnitude of π
sub three.

Since the body is in
equilibrium, we know that the vector sum of the three forces must be equal to
zero. We also know that this means we
can represent the system as a triangle, where the lengths of the triangle are
proportional to their magnitudes. This means we can treat the two
force magnitudes as if they were lengths and use the Pythagorean theorem to find
the missing magnitude. That is, five squared plus the
magnitude of π
sub three squared equals 13 squared. Subtracting five squared from
both sides and we see that the magnitude of π
sub three squared is equal to
144.

Finally, we take the positive
square root. Remember, we donβt need a
negative root since a magnitude, by definition, is positive. The magnitude of this force is
12 newtons. So, weβve found the magnitude
of π
sub three.