If Jack and Luke are on opposite sides of a canal pulling a barge with tow ropes, Jack exerting a force of 50 pounds at 20 degrees to the canal, and Luke at angle of 15 with enough force so that the resultant force vector is along the canal directly, what is the number of pounds with which Luke must pull and the magnitude of the resultant?

CI said 50sin(20) = (Luke's Vector Magnitude)Sin(15)

Divide both sides by Sin(15) and got 66. Can anyone confirm this?

And also how do I find magntiude if the vectors are connected at their tail points? I assume you just add 50cos(20) and 50cos(15)? Is this right?

And also, if you are pulling a wagon with a force of 20 pounds on a handle that maes 30 degrees with the horizontal, what is the work if its pulled 100 feet up an incline that makes an angle of 30 degrees with the horizontal?