Understanding the Laws of Sine and Cosine

  • Context: High School 
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    Laws Sine/cosine
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Discussion Overview

The discussion revolves around the Laws of Sine and Cosine, focusing on requests for proofs and explanations of their meanings. Participants express a desire to understand these laws better, particularly in the context of triangles.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant states the formulas for the Law of Sine and Law of Cosine but expresses uncertainty about their proofs and meanings.
  • Another participant suggests using the Law of Sines in relation to the area of triangles and proposes a method involving right-angled triangles to derive the Law of Cosines through the Pythagorean theorem.
  • A third participant indicates a lack of understanding and requests a demonstration of the proofs for both laws.
  • A fourth participant mentions having learned about these laws from a friend but does not recall the details, seeking assistance.

Areas of Agreement / Disagreement

Participants generally express a lack of understanding regarding the proofs of the Laws of Sine and Cosine, indicating that multiple viewpoints exist on how to approach the explanations, but no consensus on the proofs themselves is reached.

Contextual Notes

Participants have varying levels of familiarity with mathematical concepts, and there is an expressed need for clarity on the proofs, which may depend on different interpretations of the laws and their applications.

Who May Find This Useful

Individuals seeking to understand the Laws of Sine and Cosine, particularly those looking for proofs and deeper explanations of these mathematical concepts.

manbush
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Law of Sine = Sin A/a = Sin B /b = Sin c/c

Law of Cosines
a^2=b^2 + c^2 - 2bc Cos A

I used to know how to "prove" both of these laws but I haven't touched math for years.

Can someone "prove" them or "explain" what these laws exactly mean?
 
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As for the law of sines:
Use the sine law for the AREA of triangles in a clever way!

As for the cosine law:
Make a triangle with acute angles, draw its height h, so that you have two right-angled triangles.
Fiddle around with the Pythogorean theorem until you stumble upon the law of cosine
 
Sorry, I don't understand either. I been away from math too long. I know I could just use these formulas but I want to see the "proof".

Is it possible you could show me an example of proving them?
 
My friend taught me this...dont' quite remember, i would appreciate any help :D
 

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