vectors magnitude

Question

I do not understand how to set up the following problem:

"Forces of 20 lb and 32 lb make an angle of 52 degrees with each other. find the magnitude of the resultant force."

An actually picture would really help.

Answer 1

Draw a parallelogram with 2 parallel sides of length 20 and 2 parallel sides of length 32.  Two opposite angles have measure 52° and the other two have measure 180°-52° = 128°.  The length, L,  of the diagonal opposite the 128° angles is the magnitude of the resultant.

 

By the Law of Cosines, L² = 20² + 32² - 2(20)(32)cos128°

 

                                             = 400 + 1024 - (-788.047)

 

                                             = 2212.047

 

                                         L ≈ √2212.047 = 47