Vectors problem (part 2 with work)

[MarieWynn]

Homework Statement

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.
DATA: α= 47.5o β= 56.6o |A| = 7.9 cm. The vector A - B is parallel to the -x axis (points due West).
A) Calculate the y-component of vector B. Answer: -5.82 cm
B) Calculate the x component of the vector A - B .
C) Calculate the magnitude of the vector A + B.

Homework Equations

I.) B_x=B*cos(beta)
II.) B_y=B*sin(beta)
III.) A_x=A*cos(alpha)
IV.) A_x=A*sin(alpha)
V.) C_x=A_x+B_x

The Attempt at a Solution

The original problem doesn't give B, but does tell you that A_y=B_y, so you should be able to take B_y from the first part of the question and plug that value into equation II and solve for B, which allows you to use equation I to find B_x and then find A_x and add the two together to find the X component of vector A-B. The answer I came up with was 5.34 + -3.84 = 1.50. This is incorrect but I am not sure where I am going wrong. I've tried it a couple of different ways in case I was misunderstanding the meaning of A-B and all of the different ways to add those two together (or even subtract) are wrong.

 

[MarieWynn]

Got past part 2 but not understanding why part 3 isn't correct. To find the magnitude of A+B you first have to find the X and Y components of B. A_x is 5.34. A_y is 5.82. B_x is -8.83 and B_y is -5.82. So when you use the pythagorean theorem to find C, you get the square root of [(5.34 + -8.83)² + (5.82 + -5.82)² ] which is 3.49. This answer is incorrect though. I've done the math over and over again but can't figure out where I am going wrong. Am I using the wrong formula?