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## Homework Statement

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.

## Homework Equations

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.

R

^{2}= A

^{2}+ B

^{2}

Lastly, I came across this equation.

c

^{2}= a

^{2}+ b

^{2}- 2abcos(c)

## The Attempt at a Solution

I have tried all 3 equations.

1) R= 20 + 35= 55

2) R

^{2}=20

^{2}+35

^{2}

R

^{2}= 1625

R= (sqrt 1625)

R= 40.3112887

3) R

^{2}= 20

^{2}+ 35

^{2}- 2(20)(35)cos(60)

R

^{2}= 1625-1400cos(60)

R

^{2}=1625-933.71

R

^{2}= 691.29

R= 26.2923943

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