PreCalculus - Trigonometry: The Law of Cosines (15 of 15) Heron's Formula Proved

Visit ilectureonline.com for more math and science lectures!
In this video I will prove Heron's Formula.

[@sarahmanchester4510]

Very nicely presented - clear & easy to follow! I will definitely share with my geometry students.

[@aejahrojas2926]

this was absolutely amazing! You saved me for my trigonometry project !!!!!

[@Golden_Tortoise]

Wow that is impressive. "We WANT to get to this" then "we WANT to get to this," etc. to get to the simplest form type of logic takes an impressive amount of knowledge and forward thinking. Really for any proof.

[@QuintinMassey]

I was about to ask why (1-cos^2(c)) equal to (1-cos(c))(1+cos(c)), but then realized that: (1+cos(c))(1-cos(c)) = 1-cos^2(c) by distributing out the left side. Totally thinking out loud :)

[@MichelvanBiezen]

Great that you figured it out.

[@filipgenovski]

Very well explained. Thanks!

[@ptyptypty3]

Okay, Michel.. I came back and rewatched this Video!! AMAZING how clear and concise your presentation style is. Well Done!! My cat watched it with me and she has a question for you: "Meoowww.. mew mew.. Meowww ??" :)

[@MichelvanBiezen]

Hi Philip. Now if you had told me that your cat understood it as well, I would have my doubts. (Our cat is dumber than a door nail).

[@canman5060]

My most favourite proved !

[@yuhema9779]

AWWW it's such a beautiful derivation! Who first invented this was surely a genius!

[@MichelvanBiezen]

Yes there were some very smart people throughout history.

[@TiktokCreator-fo6ye]

Amazing solved sir

[@MichelvanBiezen]

Thank you. Glad you liked it. 🙂

[@reemnasser5989]

Really thank you 🙏🏻

[@MichelvanBiezen]

You’re welcome 😊

[@ahmedbaig7279]

I will say excellent because its the 5th deminstration to prove the Haroo's farmula. Wht we can nit f7nd the c8s angke.

[@thevibe8065]

why do you write a^2+b^2-c^2 except (a+b)^2-c^2 at 8:52?

[@MichelvanBiezen]

Just substituting 1 + cos C and 1 - cos C

[@thevibe8065]

Michel van Biezen thanks!

[@ptyptypty3]

I just figured out HOW Heron aka Hero Of Alexandria discovered this.. it's simple... he did NOT have a Cell phone, a Computer, a Car, a Calculator, he did not have electricity or distractions... he had Lots of time on his hands with little to No Distractions..... That's how he figured it out.. :)...

[@MichelvanBiezen]

isn't that how anything gets done? Time and perseverance with little distraction. Sounds like a recipe for success.

[@shivbabasongs181]

Nice video sir .......😆

[@user-zi2ld3dq4b]

Excellent Sir. Can this formula be proven the same way if our original triangle has an angle of more than90°?

[@MichelvanBiezen]

Yes, it works for any angle

[@davidbrisbane7206]

Yes, as sin(C) is positive for 0° < C < 180°, so this proof works for acute angles of C as well as obtuse angles of C. If you prove Heron's formula using only Pythagoras' theorem, then you need to prove it seperately when angle C is acute and then again when angle C is obtuse, so you need to do the proof twice, although the proof approach is the same in both cases. Now, since Heron was around at the dawn of Christianity, he would have used the Pythagoras' theorem to prove his famous formula.

[@user-zi2ld3dq4b]

@@davidbrisbane7206 thank you for the explanation. Good luck.

[@davidbrisbane7206]

@@user-zi2ld3dq4b All good 👍

[@puneethsupreethaa2674]

Hats 🎩 off

[@jannahreminders4310]

easy and enjoyed...

[@saitejareddy3491]

Where is previous one

[@MichelvanBiezen]

Which "one" are you asking about? Thanks,

[@mrrashedali]

thank you very much

[@chris14091975]

thx for posting

[@potrkca]

this proof is mindnumbing!

[@mrrashedali]

i have one question what is you major

[@MichelvanBiezen]

When I was a student my major was physics.

[@mrrashedali]

you are really clever teacher you know everything physics math astronomy chemistry