What did I do wrong? Two-Dimension Vectors

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The discussion revolves around a physics problem involving two-dimensional vectors related to a woman's movement. The poster expresses uncertainty about their calculations for displacement after walking specific distances at given angles. They initially believe their answer differs from the booklet's solution, which states a displacement of 165.4 m at 2.5° E of N. Responses clarify that the calculations were likely correct, but the poster may have misinterpreted the angles and components involved. Ultimately, the consensus is that the booklet's answer is accurate, and the poster acknowledges mistakes in their approach.
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1. Homework Statement
So the problem is:
A woman walks 440 m at 50° S of W and then 580 m at 60° N of E. The entire trip required 15 minutes.
A. What was the total distance (I already got the answer to this)
B. What was the displacement of the woman?

Homework Equations


I'm almost positive I did everything right. The only two things I could think of is that I mislabeled or miscalculated the equation/triangle, or it's possible that the answer in my booklet is wrong (this has happened before since my physics teacher used online resources which don't always have the right answers.) however I want to make sure it's not just me.

I have a quiz today based on this and the previous lesson so I need a reply quick.

The Attempt at a Solution



The answer in my booklet says: 165.4 m at 2.5° E of N. Is this right?
[/B]
Here is what I had written:
http://orig05.deviantart.net/276d/f/2016/287/9/d/untitled_by_shelilla-dakysaj.jpg
I separated the two angles into different triangles just like we did in lessons. However since it's such a big series of equations, unless I'm a physics expert I can't tell just by looking if I did something wrong, and if I try to revise it there is so many things that can change the answer so it's too confusing to try.
 
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You've used the Ay component in your calculation of x and Ax in your calculation of y. X directions should be east or west, and Y directions north or south.
 
Booklet is right...
What does 60 degrees north of East mean ?

[edit] Gn is right; I was wrong-footed by your drawing; the numbers are OK.
 
gneill said:
You've used the Ay component in your calculation of x and Ax in your calculation of y. X directions should be east or west, and Y directions north or south.
Crap, you're right. I probably shouldn't have started this assignment at 9, I made a few mistakes in other questions (such as sin-1(# + #) instead of sin-1(#/#) ) lol, thanks for pointing that out!
 
Glad to help. Good luck with your studies!
 

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