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.
If you like this video, consider subscribing to the channel or consider buying me a coffee: www.buymeacoff.... Thanks!
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:
• Law Of Cosines II (vis... or
• Law Of Cosines I (visu...
#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:
manim.community

[@luukaskyronlahti5205]

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

[@MathVisualProofs]

Glad they assist in understanding!

[@ajc2766]

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?

[@MathVisualProofs]

I have two law cosines. I like this one better : th-cam.com/video/NHxJ3Z_58Lw/w-d-xo.htmlsi=9nvewpvys80fjNGg . No tangents yet. Maybe someday

[@JordanHess.]

This is a very clear visual demonstration! Thank you.

[@MathVisualProofs]

Glad it was helpful!

[@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.

[@MathVisualProofs]

Yes! I’ve seen that one. Sometime I’ll try to get around to it. Full course in Euclidean geo would be nice but would take quite a bit of time I think. Thanks for the suggestion.

[@LetsFindOut1]

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?

[@MathVisualProofs]

Those are different “h” values. I should maybe have used a different letter for the second case to be more clear. But you are right that the name doesn’t matter as that value is used as an intermediate value to get the desired ratio equality.

[@LetsFindOut1]

@@MathVisualProofs awesome thanks for clarifying. and again excellent visuals and explanation. top tier stuff

[@DrWeselcouch]

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

[@MathVisualProofs]

Thanks!

[@LittlePaimon]

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

[@MathVisualProofs]

👍

[@L-vr4wg]

YOU even dare to reply here?It's you that stole his video and uploaded onto Chinese netwrok.

[@mrbb4238]

A big thank to you!🎉🎉

[@MathVisualProofs]

Welcome 😊

[@rayaneaoussar8040]

Thank you for these amazing videos ❤️!!

[@MathVisualProofs]

Thanks for checking them out.

[@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!

[@MathVisualProofs]

Yes, was interesting that they could prove PT with just this fact (as it is one of the trig facts that is not equivalent to PT).

[@hamzahabdulqadir7171]

​@@MathVisualProofswhat are you talking about please? I'd like to know.

[@boredomgotmehere]

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

[@MathVisualProofs]

The sine measures the y-coordinate on the unit circle after rotating angle A. If you rotate 180-A you end up on the same half plane so the y-coordinate is the same as that if rotating angle A.

[@boredomgotmehere]

@@MathVisualProofs that was super helpful. Thank you

[@mathsaffairs]

Hi,
Your work is awesome....
Can you tell me the name of software(s) that you use in your videos?

[@MathVisualProofs]

I use manim from 3blue1brown

[@mathsaffairs]

@@MathVisualProofs firstly, thanks for your reply....
And secondly, I guessed the same as you mention....
Your programming is simply fantastic....
Your work is very useful for TLM.....
May God Bless You My Dear....

[@MathVisualProofs]

@@mathsaffairs Thank you!

[@SARASWATIMATHSACADEMY]

Amazingly simple 🎉❤

[@hashimabbas3977]

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

[@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?

[@MathVisualProofs]

Right. I don’t know a source for this visual proof because it’s so standard.

[@vade248721]

I hate that you called that new side length h as well. just throws a wrench in this whole thing.

[@ladiklike9014]

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

[@beloved9]

正弦定理の美しい証明。

[@MathVisualProofs]

👍😀

[@emineacar3630]

How abouth root of something that forever root

[@pied6]

how does sin(180-A) = sin(A) ?

[@pied6]

2:15

[@pied6]

nvm saw answer on a comment. i didnt think about the unit circle at all.

[@user-gv9im2nf2s]

❤❤❤❤❤❤❤❤❤😅

[@willthecat3861]

Not a 'visual proof' at all. It's just the standard high school level proof using geometry and algebra. A visual proof doesn't use any algebra, just figures and pictures.