(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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'sresultant 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.

2. Relevant 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)

3. 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

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# Finding the resultant of two vector of an oblique triangle

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