A box is being pulled by two people. The ropes make angles of 40° and 55° with the direction of motion of the box. If the resultant force is 700 N, find the force that each ropes exerts on the box.

575.6 N at 40° 451.7 N at 55°

Step-by-step explanation:

Angles are measured from the direction of motion, so the "force made good" is the force in the rope multiplied by the cosine of the angle. If the forces in the ropes (in Newtons) are represented by x and y, then we have ...

x·cos (40°) + y·cos (55°) = 700

In order for the resultant to be in the direction of motion, the forces perpendicular to the direction of motion must cancel.

x·sin (40°) - y·sin (55°) = 0

Here, we have assumed that the positive direction for measuring 40° is the negative direction for measuring 55°. That is, the angles are measured in opposite directions from the direction of motion.

Any of the usual methods for solving systems of linear equations can be used to solve this set. My preference is to use a graphing calculator. It gives the answers summarized above.