Why is my resultant displacement magnitude not matching my calculations?

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The discussion centers on a man's calculations of his resultant displacement after searching for his dog, involving multiple directional movements. The user believes their resultant vector coordinates are correct but is confused about the magnitude not matching their calculations. They calculated the vector as (2.09899, -4.63) with a magnitude of 5.08357, but it appears incorrect. A suggestion is made to draw a diagram and solve the problem graphically to verify the calculations. Additionally, the importance of following the homework template and showing intermediate work is emphasized for further assistance.
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A man in search of his dog drives first 12.7 mi northeast, then 17.7 mi straight south, and finally 7.97 mi in a direction 30.3° north of west.

a) What is the magnitude of his resultant displacement?

okay so i won't explain everything i did but I am pretty sure i got the right numbers.
for my resultant vector i get (2.09899, -4.63). the magnitude should be 5.08357. but its somehow not the right answer and I am not sure what i did wrong.

whats weird is that i needed to find the position of this vector which would be arctan(2.09899/-4.63) + 360. which would be 294.07136 degrees. THIS IS THE CORRECT ANGLE! so then wouldn't that mean that (2.09899, -4.63) are the right x and y values?

what am i doing wrong?

thanks for any help!
 
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I'd start by drawing a picture and solving it graphically and then see if your numbers agree.

Don't forget you need to follow the PF homework template and show some intermediate work before we can help.
 

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