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21.
What is the resultant of the two vectors to the right?

A.    15.0 N 17.5o counterclockwise from purple vector.

B.    28.7 N 13.9o Clockwise from Red Vector

C.    24.1 N 28.4o counterclockwise from purple vector.

D.    30.0 N 17.5o clockwise from the red vector.

 
        
There are two ways to work this problem.

Law of Cosines

c2 = a2  +  b2  - 2ab Cos C

c = ( (18.0N)2 + (12.0N)2 - 2 x 18.0N x 12.0 N x Cos 145o) 1/2

Resultant = 28.7 N

Law of Sines

 
Sin A        Sin B
--------- = ---------
   a              b

   
                b Sin A        12.0 N x Sin 145o
Sin B = -------------- = -------------------------- = 13.9o
                     a                      28.7 N

Resultant = 28.7 N 13.9o Clockwise from Red Vector
     
Alternative Method

Set Red vector as standard at heading of 0o

Purple Vector is broken into components

0o component = 12.0 N x Cos 35o = 9.83 N

90o component = 12.0 N x Sin 35o = 6.88 N

Total 0o component = 18.0 N + 9.83 N = 27.8 N

Total 90o component = 6.88 N

Now combine into a Resultant Vector

Resultant = ((27.8 N)2  +  (6.88 N)2 ) 1/2  =  28.6 N

Heading is based on Tangent 
   

                                6.88 N
Heading = Tan -1 (------------) =  13.9o
                                27.8 N

Resultant = 28.6 N 13.9o Clockwise from Red Vector

Difference in two values is due to difference in round off error.