Final answer:
To find the resultant force of the boats, resolve the pulling forces into their scalar components and use vector addition to find the magnitude and direction of the resultant force.
Step-by-step explanation:
To find the resultant force of the boats, we need to resolve the pulling forces into their scalar components. The first tugboat pulls on the barge with a force of magnitude 4000 units of force at 15° above the line AB, and the second tugboat pulls with a force of magnitude 5000 units of force at 12° below the line AB.
By resolving these forces into their x and y components, we can then add up the components to find the resultant force. Once we have the x and y components, we can use vector addition to find the magnitude and direction of the resultant force.