Help Please! Vector Problem.

I can't figure this out for the life of me.

Vector A = 7.00 m and points 40.0o north of east. Vector B = 3.00 m and points 20.0o west of north, and Vector C = 3.00 m and points 35.0o west of south.
What is the magnitude of the resultant vector A+B+C?
What angle does the resultant vector A+B+C make with respect to the east?

So I've drawn it out and everything and I'm solving for "D" and what I drew out was some weird quadralateral(sp?). Anyways I solved for each of the Vectors and got the X Components and the Y Components. And this is what I got.

A -> Ax = (7.0m)(sin(40 deg)) = 4.5m
Ay = (7.0m)(cos(40 deg)) = 5.4m
B -> Bx = (3.0m)(cos(20 deg)) = 2.8m
By = (3.0m)(sin(20 deg)) = 1.0m
C -> Cx = (3.0m)(sin(35 deg)) = 1.7m
Cy = (3.0m)(cos(35deg)) = 2.5m

So then I added all the x components and all the y components and got the x and y components for D.
Dx = 4.5m - 2.8m + 1.7m = 3.4 m
Dy = 5.4m + 1.0m + 2.5m = 8.9m

and then I used the pythagorean theorem to get D which would be
3.4^2 + 8.9^2 = D^2
D = 9.5m

and I thought that was my answer but its telling me it was wrong. So I didn't even attempt to get the angle because that will probably be wrong to.
So yeah can someone help me please o:)
 

berkeman

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mixedtape_15 said:
A -> Ax = (7.0m)(sin(40 deg)) = 4.5m
Ay = (7.0m)(cos(40 deg)) = 5.4m
B -> Bx = (3.0m)(cos(20 deg)) = 2.8m
By = (3.0m)(sin(20 deg)) = 1.0m
C -> Cx = (3.0m)(sin(35 deg)) = 1.7m
Cy = (3.0m)(cos(35deg)) = 2.5m
Excellent job showing your work -- that helps a lot in our ability to help you.

I believe that you are just mixing up the N and E components a bit. You are using the correct method, of converting from the "polar" coordinates they give you into rectangular (E,N) or (x,y) components. Looking at your Ax,Ay conversion, I can see that you've got them backwards. Since they give you the vector A as pointing 40 degrees north of east, the x component will be the cos() term, and the y component will be the sin() term. Make sense?

Just run back through the equations and check the sin() and cos() terms. My guess is that you'll get it right.
 
Remember, you can solve this with a ruler and a protractor.
 
Thank you so much for the help. It really helped me to figure out where I messed up and after that it was pretty easy :D
 

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