Finding Vector Lengths: Can't figure out what I am doing wrong

[lanzjohn]

Homework Statement

The diagram below shows two vectors, A and B, and their angles relative to the coordinate axes as indicated.

DATA: alpha = 42.7 degrees,
beta = 60.0 degrees,
A = 6.70 cm.
The vector A - B is parallel to the -x axis (points due West). Calculate the y component of vector B.

Homework Equations

SOH CAH TOA

The Attempt at a Solution

So I can't figure out what I am doing wrong. I thought I knew these basics! ARG Anyway I got one chance left. So please let me know if I'm right

Well I found the angle of the triangle I am trying to find vecor y for. I am using the right triangle Since the sum vector (A-B) has no y-component, vector A must have the same y-component as vector B.

So:
90-42.7=47.3

cos47.3 = x/6.7
6.7 * cos47.3=x

Answer:
x=4.54367 cm

And that's it! BUT NOOOOO its not right ha. Is it suppose to be -4.54367cm because the component y is going y-? Or maybe I am just pig headed and am missing a major part in the problem.

 

[collinsmark]

Is it suppose to be -4.54367cm because the component y is going y-?

Yes, that's my guess. The y-component of vector B is point down, so that component is negative.

If you solve this problem using triangles (which is perfectly okay to do), you need to go back later and look at the vector to keep track of the directions of the components. Hypothetically, if A and/or B reversed directions (180^o), you would still end up with the same triangles. The lengths of the sides of the triangles involved would be identical to the case where directions were not reversed. So after you calculate the lengths of a given side, you need to go back and look at the vector to determine which way that side is pointing.