A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north. Using a graph, find the magnitude and direction of a single vector that gives the net effect of the car's trip. This vector is called the car's resultant displacement.
I am studying for a physics test, and this is a problem out of my textbook. The author gives the answer of the resultant to be 48 km, and the angle β, the angle between vector A and the resultant, to be 39° west of north.
From the book, because I missed class the day we went over this, I have learned that to find the resultant one simply adds vector A to vector B.
R= A + B
Also, from different physic web sites, some people have suggested the pythagorean theorem; however, I believe that only works with right triangles, not oblique.
R2= A2 + B2
Lastly, I came across this equation.
c2= a2 + b2 - 2abcos(c)
The Attempt at a Solution
I have tried all 3 equations.
1) R= 20 + 35= 55
2) R2=202 +352
R= (sqrt 1625)
3) R2= 202 + 352 - 2(20)(35)cos(60)
Obviously, none of these solutions match the one given by the author. How am I supposed to work this problem to find the right solution? As far as finding angle β, I have no idea where to start