Using the Pythagorean Theorem, it is found that the magnitude of the resultant force acting on the barge is of 86.05 newtons.
The Pythagorean Theorem states that in a right triangle with legs [tex]l_1[/tex] and [tex]l_2[/tex], the measure of the hypotenuse [tex]h[/tex] is given by:
[tex]h^2 = l_1^2 + l_2^2[/tex]
When one force is applied north/south, and the other east/west, the magnitude is the hypotenuse of a right triangle in which the forces are the legs.
In this problem, the forces are [tex]l_1 = 67, l_2 = 54[/tex], hence:
[tex]h^2 = l_1^2 + l_2^2[/tex]
[tex]h^2 = 67^2 + 54^2[/tex]
[tex]h = \sqrt{67^2 + 54^2}[/tex]
[tex]h = 86.05[/tex]
The magnitude of the resultant force acting on the barge is of 86.05 newtons.
You can learn more about the Pythagorean Theorem at https://brainly.com/question/654982
