Pythagorean Theorem proof based on Law of Sines independent of the Pythagorean identity

2023.3.30: news.math/
Pythagorean Theorem proof based on Law of Sines
independent of the Pythagorean identity:

the American Mathematical Society:

https://meetings.ams.org/math/spring2023se/meetingapp.cgi/Paper/23621

. for the 2000 years since trigonometry was discovered

it's always been assumed that any alleged proof of 

Pythagoras’s Theorem based on trigonometry

must be circular

-- that all the fundamental formulae of trigonometry

are themselves based upon

the truth of the Pythagorean Theorem.

But Ne’Kiya D Jackson and Calcea Rujean Johnson

from St. Mary's Academy High School

present a new proof of Pythagoras’s Theorem

https://en.wikipedia.org/wiki/Pythagorean_theorem

which is based on a fundamental result in trigonometry

—the Law of Sines—

https://en.wikipedia.org/wiki/Law_of_sines

https://planetmath.org/sineslawproof1

and show that the proof is independent of

the Pythagorean identity.

https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity

. video of the discoverers.

https://www.9news.com/article/news/nation-world/no-east-teens-make-pmathematical-discovery-2000-years-making/289-e89f40cb-85f8-4a55-ae3f-3ec37412d7b8