SOLUTION: Two forces of 40lbs and 20lbs on an object. The angle is 40 degrees between them. What is the angle between the Resultant force and the larger force?

To draw the resulting force, complete a paralellogram
by drawing a line through each arrowhead parallel to
the other vector.  I'll draw them in green.  Notice
the angle marked  is so marked because it
is supplementary to the  angle, and .:



Now I'll draw in the resultant R in red:



In the lower triangle we have a case of SAS, so we
use the law of cosines first to find the magnitude
of the resultant R (the red vector).







Now we use the law of sines:











Edwin