Area of a Triangle: ½absinC

More resources available at www.misterwootube.com

[@xBobz99]

I don't actually remember being taught deriving that formula. Neat!

[@factsverse9957]

It's a simple derivation actually.

[@KarachoBolzen]

Kenji Gunawan yes but you never really think about it

[@MTLTV-eu4nv]

For those of you who have been taught about resolving vectors to their horizontal and vertical components, you can imagine that side A is a vector pointing toward B, point C is the origin of a Cartesian (X/Y) coordinate plane, and side B is the positive X (horizontal) axis. The altitude is the vertical component of that vector, which is equal to the length of side A multiplied by the sine of angle C (a * sin C). Remember that the area of a triangle is equal to 1/2 * b * h, so you substitute a * sin C for h to get 1/2 * b * a * sin C. Although, I was not exposed to the idea of using trigonometry to compute the altitude of the triangle, I was easily able to figure that out without watching this video in its entirety.

[@vijayakumardhanasekaran2181]

@@factsverse9957 a

[@squarerootof-1307]

you have 314 likes as of now, which is the floor of 10pi.

[@Brian67859]

Your students, although they probably don't realize it now, are lucky kids...

[@abhimanyuvarma28]

Oh trust me, I'm sure they realize it. What Eddie Woo does is legendary.... too legendary to be unnoticed.

[@bach556]

Are they kids ? I doubt that

[@thefeof6161]

@@bach556 yeah, he is a high school teacher

[@schebbi]

@@thefeof6161 In what world are highschoolers taught complex numbers

[@colins6505]

@@schebbi Earth, we were doing complex numbers in algebra 2 lol

[@haywire3895]

I wish I had a teacher like him 😂

[@WigglyWings]

Who the f**k here doesn't?

[@snowcake2846]

My physics professor teaches like him.

[@tasnimulsarwar9189]

@@snowcake2846 lucky lucky. Anyways, happy physics for you.

[@VanilloSchachner]

I am a Mathematician myself and i sometimes watch your videos just to experience different kinds of explanations. This is a very basic one and i would most likely do it the same. But there are some other videos which I really like (maybe because I have forgotten some background information). So thumps up and go on :D

[@musilily926]

@Mayank Kumar Doubts in Maths?

[@iAmMeAndYouAreYou]

Not a mathematician but I'm studying mechanical engineering. His videos are great! As you say, for different kinds of explanations. I find I really like the visual approach he takes. Not just "this equation does this, go memorise it!" He has one about pythag and shows why a²+b²=c². Worth a watch!!

[@SeanBenson23]

As many have said, my life would have been very different had I had you as a math teacher. It inspires me to be a math teacher. Your videos have a ripple effect, Eddie. I use many concepts in my tutoring.

[@redfrommars5366]

6:47 Teacher: So far so good Student: Oh... No... 😂😂😂

[@evoman3dfx]

happy face emoji

[@isabellarush6765]

"Does that make sense?" aah omg wish all maths teachers were like you!! I would actually take A-Level you're such a good teacher!!! Thank you so much!!

[@anish7183]

are you from england

[@itachi6336]

@@anish7183I think he/she/non binary is

[@bakeymykakey]

rip wales

[@YigitmK]

Even i am a graduated engineer, i enjoy and actually learn basic principles and logic of math from your videos. Keep teaching!

[@djgulston]

I already know this, but I still love watching your videos. It's so entertaining.

[@jiren6637]

same

[@tony359]

I had the privilege to have one or two teachers which a similar passion and smile than Mr. Woo. Those teachers are the pillars of our society and we should all acknowledge their massive contribution to the world. Thank you Sir for who you are.

[@kylehudsons]

wow!!! never knew that ½absinC could be proved that easily~ i just kinda take it for granted

[@ashishkiift]

The students are so fortunate to have a teacher like you Eddie .. you are so knowledgable and approachable .. most of the people love or hate math because of the way they had been taught the subject ! Love from India !

[@mathenthusiast6635]

I LOVE YOU WHY ARE YOU SO UNDERRATED

[@affaanansari6227]

300k subs isnt being underrated

[@chewyhirai7166]

Math Enthusiast.... Also a Kpop Enthusiast??

[@rubikscuber1114]

army??????????

[@chewyhirai7166]

@@rubikscuber1114 Aye!! This is my other KZbin Account where I just focus on studying.....Srsly how can you avoid not seeing the Kpop vids and completions that pop up in recommended.

[@geekyprogrammer4831]

Underrated? This professor is one of the top ten teacher in the world. Your KPop is underrated....

[@danvindsouza2725]

*You Are one of The BEST Teacher wish you were teaching in our school*

[@sasidharputtaparthi1350]

The intensity of involvement and joy of teaching maths..... I never seen in any teacher..🙏🙏🙏

[@blank-vw2sb]

loving you Eddie woo... I wish I had a math teacher like you. great

[@3nails4you]

A great way to help remember this is that the formula is ALSO the one you use for RIGHT triangles - it's just that sin(90 degrees) works out to 1, so we don't write it in the formula.

[@ghadahalqahtani834]

Thank you For recording all these amazing lessons You'r the best teacher ever🌟

[@jayantadinda9375]

Thanks sir it helped me a lot. Your explanation was too good.

[@kanishkkaushal549]

Your videos are really cool man.....Helping me in improving my teaching skills

[@aadiesood1221]

Where do u teach Sir? I am from India. You also may be....?

[@georgeh1352]

A brilliant teacher, you should be teaching teachers Mr Woo.

[@rakshikab1980]

You are an incredible teacher... Its really nice to watch ur way of teaching.

[@justrevision6820]

Thanks again Mr Woo, Math never fails to disappoint!

[@andrewlim5523]

Wish had teacher like this when i was in college learning geometry. Very neat and understandble because the way he explains things.

[@vashisthachaturvedi3257]

Hi. I really like the way you make students understand. Just 1 request.May you make a video on the relationship between rhombus' side and diagonal

[@fordprefect1925]

you're a great teacher. Wish i had you instead of my maths teacher.

[@vishalshow295]

Hello Sir, I am an also Math teacher from India. Your Videos are very helpful by which I teach my students. thank you for making the free video. Can u provide us the materials and formula sheets pdf which you mentioned in the video, it will be very helpful... thank you once again for the videos....

[@r1234233]

Is it strange that I watch you're videos for fun.... I'm gonna be so good at math now, thank you oh mighty math guru!!!

[@shadowhunter241]

I see triangles and an eye....

[@sangeethasenthil2174]

David Robinson illuminati!!!!!

[@infinitesimotel]

iloominati konfirmed ! LMAO

[@ceridwenmae5206]

shat

[@Gmtz01]

Savage...

[@imtiazahmedshaikh5367]

u have good sense bruh

[@Phillycrake]

These videos are awesome!

[@dcs_0]

I did the Intermediate Maths Olympiad last Thursday, and one of the questions required this formula. I forgot the factor of 1/2 D;

[@reznovvazileski3193]

My math teacher used to mess us up even harder by giving us everything except the included angle so we had to work that one out knowing the sum of the angles = 180deg in a triangle xD He didn't nearly explain it as well as you do though.

[@lohgock_y]

Really nice explenation! Hey, im wondering, does the formula also work with a triangel, that has an angle of more than 90 degrees and your missing the hypotnuse? Cuz you would kinda draw a triangle outside the triangle which only shares one side of the original one

[@pepijnvandaalen8851]

He can exlain like everything so clearly

[@pepijnvandaalen8851]

Explain but whatever

[@monoman4083]

you explain the basics.good, good good..

[@CletusBoyce]

I knew the answer before Eddie showed it. Whahoooo I can do high school trig. Finally! 🤓

[@sakmannakki7294]

over HEAAA

[@karlcorrz]

Sakman Nakki *NAO OVA HEIA*

[@claireli88]

If the length a,b and c of all the 3 sides of a triangle are known, we can still find its area by this formula A = sqrt{s(s-a)(s-b)(s-c)} where s = (a+b+c)/2.

[@JashXD]

yes that’s heron’s formula

[@krishnvi164]

Hey sir , I am from India and I am biggest fan of your teaching ,😊😊🙈

[@seanpeters8551]

pretty sure if i had this guy as a math teacher, i wouldnt be majoring in biology

[@Subhajit_Paul123]

What is wrong with biology? It is an interesting subject as well.

[@antwidavid389]

Naaaahhhhhh my mind is blown😮🔥🔥

[@dildobaggins2759]

I feel like ime part of the class on a Sunday morning this is fun...

[@Qermaq]

You noted that it should not be a right triangle, but you didn't mention that this formula will also work for any right triangle UNLESS c is the hypotenuse (as if c is the hypotenuse, C=pi/2, and sin(pi/2)=0, this formula would give an area of 0 in this case). If you use a leg as c it'll work super. As a, b and c are given, could just use Heron's Law and no trig needed. ;) I know, it's a trig class. But Heron is the most powerful tool for area if you know all the sides.

[@leoyang1.618]

Love it!!!!

[@SkeleCrafteronYT]

MIND BLOWN

[@putindavid1911]

Every time I see your videos I fell like I want to become your student....

[@johncormier]

We learned this stuff at breakneck speed. Our teachers aren't give much time to reach this stuff. I wish math was more like this.

[@rishiraj1986]

Which grade he teaches 😯😯

[@leonidmiroshnik9542]

Rishi Raj all of them

[@hinducatalyst9331]

Really a Richard Feyman in mathematics....

[@lavendalee7692]

Awesome maths teacher.

[@angelstarfire]

That's awesome! Thank you!

[@TheActurialRepository]

You are a great guy

[@RonBrumleve]

I think what the latter student may have intended by her question is, "What if you know sides a and b and angle A" - how then would she calculate the Area of that triangle without knowing its height?

[@MHSTAR-ej8cj]

This is amazing, can I have the pdf of the formula sheet? It will help me ❤️

[@paulg687]

Its very nicely presented - he's a good teacher. However, one thing I'd point out is this is the area of half the triangle not the full triangle drawn. You could easily have drawn a right angle triangle, wrote the formula A = 1/2 b * h and replaced h with a sin x by the trig definition (which is effectively what been done but inside a bigger triangle). Maybe this way shown was to be used later for something else?

[@tjs001]

Sorry, but that's incorrect. It's the area of the large triangle! Maybe you missed that he is simply substituting an alternative to 'h' into the original 1/2 base X height formula for the large triangle. Maybe just do it yourself on paper and you should see it's right.

[@paulg687]

tjs001 I think you may have misunderstood my point. The point is he drew a triangle and created another triangle from it - a right angle triangle. There was no need to create the first triangle. He could have simply created a right angled triangle. The area is correct- for the right angle triangle - not for the big triangle that he dissects to create the right angled triangle from.

[@tjs001]

@@paulg687 Paul, you still seem to be saying that he has created a formula for just the right-angled triangle, when he has derived a formula for the the large, irregular one - in fact, any triangle. That was the whole point of drawing the initial triangle - to derive a formula for finding the area when it's not right-angled. Someone else said the same as you further down in the comments, and he was corrected by another poster giving a similar response as mine. I wonder if you're thinking the 'b' in the formula refers to the base of the right triangle. It doesn't - it's the side of the large triangle labelled 'b'.

[@paulg687]

@@tjs001 Yeah sorry, I totally messed up what I meant to say. That was wrong, I was confused with a different video! I was trying to explain that the area defined for the triangle A=1/2BH should be derived to explain how that is derived and not just shown, since this is the area you are defining but in terms of sin. He shows how the right angle triangle is defined but not the regular triangle. So: A = 0.5 (AD)(BD) + 0.5(DC)(BD) A = 0.5(BD)(AD+DC) A= 0.5(AC)(BD). Or 0.5 BH as he's defined. (D is the intersection of the perpendicular line creating 2 right angle triangles). Now you sub sin in that and get the formula You were totally correct, sorry.

[@sihamkessar4295]

Very good explanation

[@rajmfh]

I wish i had a teacher like you when i was in school

[@zouzou6164]

if i had to have anyone teach me maths this guy would do the job perfectly

[@bibi66966]

Thank you Eddi, your videos are helpful, however, I prefer the explanation to be always on the big whiteboard

[@harsharoy1368]

Yeah components i love those

[@joshlucas4269]

Wouldn't that forumula only give you half of the orignial triangle? So you would have to work out the other half aswell?

[@FootballPsychoPS3T]

Josh Lucas The area of the entire triangle is ½bh. I hope that that is clear. The way that the formula is derived simply replaces the h term with asinC. Since asinC = h, it can be replaced to get the area of the entire rectangle. The area of the red triangle would have a base length that is smaller than the entire big triangle.

[@sdhoang]

Don't need to go to math class, just see this guy videos

[@tuckercoffin2164]

Me: randomly learning math on Sunday because of how fun these videos are

[@sodiboo]

what if i don't have the angle but the side length of c? 3 side lengths can only represent 1 triangle, right? so i should be able to get the area, but how do i get the angle between a and b then?

[@9308323]

Not sure how much you still need it, but for your question, you're gonna have to use a different formula, which is called Heron's Formula.

[@ali-khan]

I have no idea what you are saying but I'm engaged the whole time

[@benkd7521]

wow i learned so much in few minute thank you sir

[@PatClevenger0709]

You could have pointed out that in a right triangle, the included angle is 90°

[@picklerick5094]

It really sucks here in Malaysia we don't have teachers like you and we also seperate our Mathematics into 2 different subjects, 1 being the the basics and the other is calculas, trigonmetry etc.. All they ever each us is just memorise and apply during test, they never want us to learn and we are given only 2 years to cover all the complicated ones.

[@ExtrusionXDesigns]

wtf there is? im from malaysia and theres no such thing tho, what grade are you in?

[@syringe2925]

thailand,also

[@dinmarlinwelcabural6509]

I never heard this formula, i only know the Herons Formula. Can someone tell me the difference of herons formula and this one if there is?

[@eTech9300]

Heron's formula uses only the side lengths to calculate the area; this one uses two side lengths and the measure of the angle between them. Hope that helped.

[@dinmarlinwelcabural6509]

Eli Cole so u mean i can use either of the two and come up with the same answer?

[@eTech9300]

@@dinmarlinwelcabural6509 Right- the area of the triangle is the same regardless of which formula you use to calculate it. The choice to use this or Heron's formula just depends on what information you have to work with.

[@JabbaWockeez_]

I wonder if he would have made it easier for me on math - college level

[@CletusBoyce]

Eddie Who is my hero. 🤓

[@vaishnav4035]

You are a genius 😍😍

[@zz-gz6yt]

how do u know the value of the angle C

[@Quantum_Magnus]

This has to do with the Law of Sines/Law of Cosines.

[@entropy5157]

Why not just use Pythagoras thm to find out h nd find the area with the basic formula???!! If we know a,b finding h is easy!

[@rhpmike]

I think you'll find that if you review the Pythagorean Theorem, it requires a right angle and this is specifically for when you do not have a right triangle.

[@protaotogamer1503]

epic video

[@jonathan3504]

But what happens if I have a triangle in which I am only given the measures of a, b, and c, but no measures for any angle? Can I still find the area of the triangle? (Assuming that this is not a right triangle)

[@SanjeevKumar-js4mu]

Use herons formula

[@brandonperkins9282]

This guy can go through all that in 10 minutes yet my teacher would take lessons and I’d still understand it less than I do now

[@camiloperezchaves9895]

Good damm matgs are amazing

[@saiavinash7432]

its better to have just 2 pieces of information b and h than to have 3 b h and angle c cause you know simplicity is nice

[@SureShot55]

Hello sir. I have a question that how would I be able to find 'SinC'? Will it be given in the question or something else...? I'm a little confused. By the way another great lesson. Thank You.

[@carultch]

Either the angle C would be given, or enough information to get the angle C would be given. Then you enter it in the sine function on your calculator, to get sin(C), making sure the calculator's angle unit is in the mode that is consistent with your problem. You might be given the other angles instead of angle C, such that you need to use the 180 degree rule for triangles to get angle C. Or you might be given all three angles, such that the other two angles are red herrings and not needed in the problem.

[@snow9920]

Can I grab a copy of your formula sheet badly needed :

[@xid17vishwarajsharma11]

Actually not a rectangle but a parallelogram.

[@smartypants1804]

thank you sir😃

[@kabirwaljee8685]

also area = 1/2 bc sin A = 1/2 ac sin B also works for obtuse angled triangle where altitude is outside the triangle. This could have made more interesting for the students. Great job Mr. Woo. I am 72 and just discovered your channel.

[@shivaranjan1825]

Hey there, Tan C = h/b h= b×tan C If c --> π/2 What happens to h and a in Eddie's triangle

[@Faisal-os9ks]

Than the triangle would become a line, as pi/2 radians is 180 degrees, the sum of all angles in a triangle.

[@tushurawat6001]

6:21 is the best moment

[@birendersingh5943]

I want to know how will you calculate sin c if it has any random value say 24? Any help would be great

[@factsverse9957]

Use a calculator 😂

[@yeetoryeeted5363]

Can u teach me everything plz

[@beautay4472]

Just watch em vids! :D though you probably already have :)

[@phicoding7533]

I wish I had him

[@michealryan23]

800k followers and no adverts. Wow

[@Proccito]

I think I missed something: How is that the whole triangle? I saw him splitting it in two, but what if those two triangles arn't the same?

[@bolanleaderoju1127]

Great

[@sameerhussainsiddiqi8794]

Why not using tan and cos...why only sin

[@carultch]

Because the side we know is the hypotenuse, and the side we want is the opposite side. Hence opposite/hypotenuse is the ratio that matters for this problem.

[@lgcyadam4323]

do u do tuition

[@skdaroch]

Some idiot student is making noise to such a good lecture. As our teacher once said “not everyone should actually be educated to graduate / masters because we need someone to make our roads, clean toilets, etc”.

[@lipushaila5466]

Note to Myself: মধ্যবর্তী কোণ ↔ Included Angle

[@monoman4083]

i can't see your mic but the sound is ok.. the white board is too low, claim compensation for bodily injuries...

[@alim7532]

You shoulda showed them in a right angle triangel sin 90° =1 therefore the sin C is not written.

[@beautay4472]

I can bet you that the 40 people that disliked this video are not very smart :o

[@nanito6805]

Mi incantin lastenichon matenumereichon