Solve Vector Problem: Find Magnitude & Angle of A+B+C

[mixedtape_15]

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

 

[berkeman]

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.

 

[civil_dude]

Remember, you can solve this with a ruler and a protractor.

 

[mixedtape_15]

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