What did I do wrong with these vectors?

[Newphysicsguy]

Find $\vec{a}+\vec{b}$ (Look at the picture)

The book shows the solutions as :
a. 4.1m Along the +x axis.

I however do not know where I went wrong in my calculations.

$\vec{a}+\vec{b}=\begin{bmatrix} a_x+b_x\\ a_y+b_y \end{bmatrix}=\begin{bmatrix} |\vec{a}|\cos(30)+|\vec{b}|\cos(45)\\ |\vec{a}|\sin(30)-|\vec{b}|\sin(45) \end{bmatrix}=\begin{bmatrix} \frac{3\sqrt{3}}{2}+\sqrt{2}\\ 1.5-\sqrt{2} \end{bmatrix}=\begin{bmatrix} 4.01\\ .085 \end{bmatrix}$NOTE: If I posted this is the wrong location I am sorry. This is not homework, I am doing it on my own time.
EDIT: thank you for moving my post to the correct location.

 

[jtbell]

Check your calculation for $a_y$.

 

[Newphysicsguy]

That was a typo, it should be 3sin(30) which comes to be 1.5 which I had in the 3rd step. Sorry for the typo. Unless I did it wrong anyways? Either way $a_y$ does not effect $a_x+b_x$ which is also off from what the book says.

 

[jtbell]

You're right, your numbers in the next to last step are OK. I noticed it while you were writing your latest post. As far as I can tell, your answer is OK. Whoever wrote the answer you were given, didn't round it off correctly or consistently. To one decimal place, the components should be 4.0 and 0.1. To zero decimal places, they should be 4 and 0.

It's probably a typo for 4.01 instead of 4.1. Those things do happen. I've seen it lots of times.

 

[Newphysicsguy]

Thank you. I am never sure if I am wrong or if the book is wrong. It's better to always assume I am wrong.