Use the cosinus law to prove this formula

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Homework Help Overview

The discussion revolves around using the cosine law in the context of triangle ABC, where angle B is 60°. The original poster seeks assistance in proving a specific formula related to this triangle.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the cosine law and its application to the given triangle, questioning how to manipulate the law to fit the problem's requirements. There are inquiries about solving for specific sides and the implications of switching angles and sides.

Discussion Status

The conversation includes attempts to clarify the cosine law and its application, with some participants providing specific formulations. There is an ongoing exploration of how to integrate the original formula into the derived expressions, though no consensus on correctness has been reached.

Contextual Notes

Participants express uncertainty about the correct application of the cosine law and the implications of switching angles and sides in the triangle. There are references to external resources for formulas, indicating a reliance on established mathematical principles.

Mewtwo
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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?
 
Last edited by a moderator:

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