Question

The resultant of two forces acting on a body has a magnitude of 80 pounds. The angles between the resultant and the forces are 20Á and 52Á. Find the magnitude of the larger force.

Answer 1

To find the magnitude of the larger force, use the concept of vector addition and the law of cosines.

Step-by-step explanation:

To find the magnitude of the larger force, we can use the concept of vector addition. We have the magnitude of the resultant force and the angles between the resultant and the forces. Let's call the larger force F1 and the smaller force F2.

Using the law of cosines:

F1^2 = F2^2 + 80^2 - 2 * F2 * 80 * cos(52°)

By substituting the value of F2 from the equation above, we can solve for F1. Once we find F1, we can calculate F2 by subtracting F1 from the magnitude of the resultant force (80 pounds).

Answer 2

The basic idea is that you form a parallelogram with those two vectors as the two different side lengths another way to see it: start at the tip of one vector and move in the same direction as the other vector (and the same length as the other vector)

With any parallelogram, the adjacent angles are supplementary

180-52-20= 108 degrees