Physics magnitude and direction?

[amber_hsk]

I know this is basic stuff, but if anyone would be willing to help... :)
At a certain time, a car is 150 meters due west of your house. If it is traveling with a constant velocity of 30m/s 30 degrees south of east, what are the ,magnitude and the direction of its position relative to your house 5 seconds later?

30m/s(5s)=150m

150cos30= roughly 130 m
150sin30=75m

150m-130m=20m

mag=sqrt((75^2)+(20^2))=77.6m

tan inverse(75/20)= 75 degrees

So, the car is 77.6 meters away from the house at an angle of 75 degrees, south of west.

Does that seem correct?
Thanks

 

[TSny]

Welcome to PF!

Your answer and method of solution look correct to me.

 

[amber_hsk]

Welcome to PF!

Your answer and method of solution look correct to me.

Thanks! :)
Though, should it be inverse tan (20/75)=15 degrees in the last part because the answer in the book was 15° west of south?

 

[SammyS]

Thanks! :)
Though, should it be inverse tan (20/75)=15 degrees in the last part because the answer in the book was 15° west of south?

Yes, tan^-1(20/75) ≈ 14.93° .

 

[TSny]

Thanks! :)
Though, should it be inverse tan (20/75)=15 degrees in the last part because the answer in the book was 15° west of south?

75^o south of west is the same as 15^o west of south. So, either way of expressing the answer is fine.