Calculating Y-Component of Vector B: Solve Vectors Question

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SUMMARY

The discussion focuses on calculating the y-component of vector B given vector A and specific angles. The key data includes α = 47.5°, β = 56.6°, and |A| = 7.9 cm. The relationship A - B being parallel to the -x axis indicates that the y-components of vectors A and B must cancel each other out. Therefore, the y-component of vector B can be determined using the equation By = Bcos(β), where B must be derived from the context of the problem.

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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). Calculate the y-component of vector B.

Homework Equations


By=Bcos(theta)


The Attempt at a Solution


I haven't attempted this yet. What I need help with is setting it up, not actually solving the problem. I feel like some data is missing. In order for me to calculate the y component using the formula listed above, I need to know B. But I am only given A. So how do I find B? I can't find it anywhere. There are other parts to this question but I think I can handle those once I get B. Can someone help me figure out what I am missing here? Thanks :)
 
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Think about it like an algebra problem, instead of giving you A and B and asking you to find the result (lets call it C), they're giving you A, and telling you something important about the resultant (C)---i.e. note that they say A-B is parallel to the -x axis, what does that tell you?
How can you use that information?
 

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