Law of Sines Visual Proof

This is a short, animated visual proof of the Law of Sines using the definition of sine and by dropping appropriate altitudes of the triangle for given angles. The altitude may intersect the opposite side or an extended segment of the opposite side.

This animation is the classic visual proof the fact but most likely not the one Euclid used.

For visual proofs of the Law of Cosines, check out:

#mathshorts #mathvideo #math #trigonometry #lawofsines #triangle #manim #animation #theorem #pww #proofwithoutwords #visualproof #proof #circle #obtuseangle #acuteangle #angle #trigidentities #identity #righttriangle

To learn more about animating with manim, check out:

[luukaskyronlahti]

i understand best with visuals so i really enjoy your visual proofs!

[HIDEY_RUNNYpigs]

But h from the first part is shorter than h from the second part so how will they be equal?
Edit: It's because while h=asinB=bsinA that doesnt mean h=a/sinA

[nonridiculousadjective]

Love this, I keep coming back every time I need a refresh since it's all done in just 2 mins. This time I remembered to also like and sub.
Thank you so much!

[the_hidden_library]

Surely you are aware of the proof which goes via constructing the circumcircle.

Also, a suggestion, please consider delivering a full course in Euclidean geometry. Would be great for high school students.

[ajc]

This is amazing! My teacher used a different visual proof to prove the law of sines but it was extremely confusing and hard to follow. This proof is so much easier! Are you going to make one for the law of cosines and the law of tangents?

[JordanHess.]

This is a very clear visual demonstration! Thank you.

[DrWeselcouch]

Wow this is great! I wish I was shown this back in high school. It would have blown my mind.

[LetsFindOut]

Beautiful visuals and explanation, but does the second variable "h" have to be equivalent to the first variable "h"? or does it not matter because you're simply using it to relate the "sin B divided by B" ratio to its counterparts for A and C?

[boredomgotmehere]

Great one. Thanks so much. Just wondering, how is Sin (180 - A) = Sin A ? at @2:15

[hashimabbas]

But u haven't proved that all these equal to 2R

[rayaneaoussar]

Thank you for these amazing videos ❤️!!

[mathsaffairs]

Hi,
Your work is awesome....

Can you tell me the name of software(s) that you use in your videos?

[SeanSkyhawk]

This is a foundational principle of that new Pythagorean theorem proof that made the news recently if I am not mistaken. Looking forward to seeing that next!

[LittlePaimon]

This certificate is truly beautiful and simple, something students can easily learn.

[axe-tqwn]

Thank you for existing.
I can’t understand anything in class.

[phiarchitect]

Another great demonstration!

But at the end, you say that this is a "standard fact known to Euclid" Perhaps, but not in this way?

[antmrdm]

so, the sine rule is came from dividing triangle with 90° line, right?

[ladiklike]

but what about the 2R?
a/sin(A) = b/sin(B) = c/sin(C) = 2R {R is a radius of circumcircle of a triangle}

[louisehulks]

Good stuff. But are you sure Euclid knew about the law of sines? I thought it was Descartes who first published it

[EarthlyYT]

how does the sin of 180-A = the sin of A. good vid none the less