Use the cosinus law to prove this formula

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The discussion centers around using the cosine law to prove a specific formula related to triangle ABC, where angle B is 60°. The original poster expresses confusion about how to apply the cosine law and seeks guidance. Participants clarify that the cosine law can be adapted by switching angles and corresponding sides when necessary. After some back-and-forth, the original poster successfully manipulates the formula and seeks confirmation on their final result. The conversation highlights the collaborative effort to understand and apply the cosine law in a geometric context.
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Hey! I have a problem here that I can't solve, help would be greatly appreciated.

Homework Statement



In a triangle ABC with sides a, b and c, B is 60°. Use the cosinus law to prove this formula:

http://www4c.wolframalpha.com/Calculate/MSP/MSP54721a0508eiidf5ddbd00005aahbcg10134ag4h?MSPStoreType=image/gif&s=34&w=147&h=47

2. The attempt at a solution

I have no idea how to solve this so I was hoping you guys could at least point me in the right direction.

-Thanks in advance!
 
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What does the cosine law state in this case?
 
micromass said:
What does the cosine law state in this case?

Sorry, but what do you mean? I know the cosine law is: http://www4c.wolframalpha.com/Calculate/MSP/MSP45341a050abcb84ib7df000067dfbce6f994ai94?MSPStoreType=image/gif&s=10&w=167&h=18 but I just don't know what to do with it. Should I solve for c?
 
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Mewtwo said:
Sorry, but what do you mean? I know the cosine law is: http://www4c.wolframalpha.com/Calculate/MSP/MSP45341a050abcb84ib7df000067dfbce6f994ai94?MSPStoreType=image/gif&s=10&w=167&h=18 but I just don't know what to do with it. Should I solve for c?

Can you state the cosine law where you take cos(B) instead of cos(A)??
 
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micromass said:
Can you state the cosine law where you take cos(B) instead of cos(A)??

So I get http://www4c.wolframalpha.com/Calculate/MSP/MSP6381a050h93gegh83bh00001796145faf9g758g?MSPStoreType=image/gif&s=35&w=178&h=18 ? Sorry if I'm slow :/
 
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And cos(60)=... ??
 
micromass said:
And cos(60)=... ??

ok 0.5 so I get http://www4c.wolframalpha.com/Calculate/MSP/MSP11051a050h26b3g19eba000052d70cgif2ch1ich?MSPStoreType=image/gif&s=16&w=112&h=18 ?
 
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Sorry, there was something wrong before that. If you switch A and B, then you also need to switch a, b and c around...
 
micromass said:
Sorry, there was something wrong before that. If you switch A and B, then you also need to switch a, b and c around...

So I get http://www4c.wolframalpha.com/Calculate/MSP/MSP48411a050dgeddd2i67000003ecabg685d804cd1?MSPStoreType=image/gif&s=18&w=112&h=18 ?
 
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  • #10
Now try to work the formula in the OP into the formula you just found.
 
  • #11
micromass said:
Now try to work the formula in the OP into the formula you just found.

ok I got this http://www4c.wolframalpha.com/Calculate/MSP/MSP44471a050d98d94cbeec000020fe90ga7i8984hb?MSPStoreType=image/gif&s=9&w=210&h=54
Is that correct?
 
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