Trigonometry: Proof of Law of Cosines (and Pythagorean Theorem)

in MES Science13 days ago (edited)

In this video I show a simple geometric proof of the cosine law. This is very useful in real world applications. Also from the proof of the cosine law you can easily proof the Pythagorean theorem as well by setting the angle equal to 90 degrees.

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Trigonometry Proofs: Law of Cosines

Trig Law of Cosines Resized AI.jpg

Geometric Proof of the Cosine Law




Corollary: Proof of the Pythagorean Theorem





To be honest, I always knew that the square of the hypotenuse is equal to the sum of the squares of the legs and for the first time I see the subtraction of the double product of the legs multiplied by the cosine of the right angle. Let's just say that I only superficially remember mathematics and geometry, and the lack of knowledge of English does not allow me to understand the video, but it's interesting to see something that I have not encountered.

Yup, the Law of Cosines is similar to your memory of the more famous Pythagorean theorem, but it's more general and works for any angle not just at right angles!
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