SOLUTION: Two forces of 40 pounds and 20 pounds, respectively, act simultaneously on an object. The angle between the two forces is 40(degrees). Find the magnitude of the resultant, to the n

 

Complete the parallelogram by drawing a line parallel to each vector
through the tip of the OTHER vector.

 

Since two adjacent angles of a parallelogram are supplementary, the
angle at the lower right corner of the parallelogram is 180°-40² or 140°



Now we draw in the resultant vector R



Isolate the lower triangle. (You could isolate the top one
just as well).  Label it triangle ABC



Solve for b (which is the magnitude of vector R, using the law 
of cosines:

b² = a² + c² - 2ac·cos(B)

b² = 20² + 40² - 2(20)(40)cos(140°)

b² = 400 + 1600 - 1600)(-.7660444431)

b² = 3225.671109

Use the principle of square roots:

b = 56.79499194

Since b is the magnitude of vector R, then
the resultant force R to the nearest tenth
of a pound is 56.8 lb.

Now we only need to find angle A for that
is the angle between the larger force and
the resultant.

The law of sines tells us that



cross-multiplying:

  

 





Use the inverse sine

       A = 13.08248883°

To the nearest degree, this is 13°

Edwin