Use the cosinus law to prove this formula

In summary, the conversation discusses using the cosine law to prove a formula in a triangle ABC where B is 60°. The formula is stated and the person asks for help in solving it. They are directed to switch A and B in the formula and then work it into the original formula. The final solution is provided and confirmed to be correct.
  • #1
Mewtwo
7
0
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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  • #2
What does the cosine law state in this case?
 
  • #3
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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  • #4
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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  • #5
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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  • #7
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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  • #8
Sorry, there was something wrong before that. If you switch A and B, then you also need to switch a, b and c around...
 
  • #9
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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1. What is the cosinus law?

The cosinus law, also known as the law of cosines, is a mathematical formula that relates the sides and angles of a triangle. It is used to find the length of a missing side or the measure of a missing angle in a triangle.

2. How do you use the cosinus law?

The cosinus law states that the square of a triangle's side is equal to the sum of the squares of the other two sides, minus twice the product of those two sides and the cosine of the angle between them. This formula can be rearranged to solve for any missing side or angle in a triangle.

3. What is the purpose of proving a formula using the cosinus law?

Proving a formula using the cosinus law allows us to demonstrate the mathematical relationship between the sides and angles of a triangle. It also helps to validate the formula and ensure its accuracy and applicability in various situations.

4. Can the cosinus law be used for any type of triangle?

Yes, the cosinus law can be used for any type of triangle, whether it is a right triangle, acute triangle, or obtuse triangle. However, the specific formula and method of using it may differ depending on the type of triangle.

5. Are there any limitations to using the cosinus law?

The cosinus law can only be used for triangles, and it is most applicable to solving problems involving triangles with known side lengths and angles. It may not be as useful for triangles with missing or unknown measurements, in which case other methods such as the sine or tangent law may be more suitable.

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