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.
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.
@@rubikscuber1114 Aye!! This is my other UA-cam Account where I just focus on studying.....Srsly how can you avoid not seeing the Kpop vids and completions that pop up in recommended.
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
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?
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.
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.
@@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'.
@@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.
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.
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.
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 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.
Those are "students"? At that age they should know much more, these classes are teached at a much younger age in many countries. On top of their poor knowledge, these young guys have no basic education, making noise and talking while teacher expose his lesson is disturbing for any decent person. Idiots...stupid and uneducated makes a great combination, bright future... Too bad, many kids would be fortunate to learn from such a modern and charismatic teacher.
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
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!!
"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!!
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.
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 !
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.
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.
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....
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.
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.
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”.
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?
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.
Your students, although they probably don't realize it now, are lucky kids...
Oh trust me, I'm sure they realize it. What Eddie Woo does is legendary.... too legendary to be unnoticed.
Are they kids ? I doubt that
@@bach556 yeah, he is a high school teacher
@@thefeof6161 In what world are highschoolers taught complex numbers
@@schebbi Earth, we were doing complex numbers in algebra 2 lol
I don't actually remember being taught deriving that formula. Neat!
It's a simple derivation actually.
Kenji Gunawan yes but you never really think about it
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.
@@factsverse9957 a
you have 314 likes as of now, which is the floor of 10pi.
Even i am a graduated engineer, i enjoy and actually learn basic principles and logic of math from your videos. Keep teaching!
I wish I had a teacher like him 😂
Who the f**k here doesn't?
My physics professor teaches like him.
@@snowcake2846 lucky lucky.
Anyways, happy physics for you.
I already know this, but I still love watching your videos. It's so entertaining.
same
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.
I LOVE YOU WHY ARE YOU SO UNDERRATED
300k subs isnt being underrated
Math Enthusiast.... Also a Kpop Enthusiast??
army??????????
@@rubikscuber1114 Aye!! This is my other UA-cam Account where I just focus on studying.....Srsly how can you avoid not seeing the Kpop vids and completions that pop up in recommended.
Underrated? This professor is one of the top ten teacher in the world. Your KPop is underrated....
Thanks again Mr Woo, Math never fails to disappoint!
Your videos are really cool man.....Helping me in improving my teaching skills
Where do u teach Sir?
I am from India. You also may be....?
You are an incredible teacher... Its really nice to watch ur way of teaching.
I knew the answer before Eddie showed it. Whahoooo I can do high school trig.
Finally! 🤓
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
Hey sir , I am from India and I am biggest fan of your teaching ,😊😊🙈
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.
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?
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.
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.
@@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'.
@@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.
pretty sure if i had this guy as a math teacher, i wouldnt be majoring in biology
What is wrong with biology? It is an interesting subject as well.
Me: randomly learning math on Sunday because of how fun these videos are
Wouldn't that forumula only give you half of the orignial triangle? So you would have to work out the other half aswell?
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.
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.
wtf there is? im from malaysia and theres no such thing tho, what grade are you in?
thailand,also
how do u know the value of the angle C
Very good explanation
Don't need to go to math class, just see this guy videos
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?
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.
Eli Cole so u mean i can use either of the two and come up with the same answer?
@@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.
I have no idea what you are saying but I'm engaged the whole time
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?
Eddie Who is my hero. 🤓
epic video
Where am I?
You shoulda showed them in a right angle triangel sin 90° =1 therefore the sin C is not written.
Generally it is not
Great
Well done Mr. Woo for keeping your calm and carrying on while these brats talk amongst themselves during class.
6:21 is the best moment
In this one mistake is their
I can bet you that the 40 people that disliked this video are not very smart :o
Dang! I always wanted to know this!! Goddamn useless teachers I've had!!!
Do the students ever shut up?
Lol we were like them in one point of our school life
(a^2+b^2+c^2)^2-2 (a^4+b^4+c^4) = area of any triangle with sides a b c
WTF .Heron`s formula is simpler
plz join teh loominati
plz i'll give u a kookie
Those are "students"? At that age they should know much more, these classes are teached at a much younger age in many countries.
On top of their poor knowledge, these young guys have no basic education, making noise and talking while teacher expose his lesson is disturbing for any decent person.
Idiots...stupid and uneducated makes a great combination, bright future...
Too bad, many kids would be fortunate to learn from such a modern and charismatic teacher.
he's a midschool/highschool teacher, student doesn't mean adult in every part of the world
Who TAUGHT you how to speak proper English
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
@Mayank Kumar Doubts in Maths?
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!!
6:47
Teacher: So far so good
Student: Oh... No...
😂😂😂
happy face emoji
"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!!
are you from england
@@anish7183I think he/she/non binary is
rip wales
wow!!!
never knew that ½absinC could be proved that easily~
i just kinda take it for granted
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.
I see triangles and an eye....
David Robinson illuminati!!!!!
iloominati konfirmed ! LMAO
shat
Savage...
u have good sense bruh
over HEAAA
Sakman Nakki
*NAO OVA HEIA*
I did the Intermediate Maths Olympiad last Thursday, and one of the questions required this formula. I forgot the factor of 1/2 D;
Thanks sir it helped me a lot. Your explanation was too good.
Which grade he teaches 😯😯
Rishi Raj all of them
Really a Richard Feyman in mathematics....
*You Are one of The BEST Teacher wish you were teaching in our school*
loving you Eddie woo... I wish I had a math teacher like you. great
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
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 !
Can u teach me everything plz
Just watch em vids! :D though you probably already have :)
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.
Thank you
For recording all these amazing lessons
You'r the best teacher ever🌟
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.
This is amazing, can I have the pdf of the formula sheet? It will help me ❤️
Can I grab a copy of your formula sheet badly needed :
Naaaahhhhhh my mind is blown😮🔥🔥
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....
The intensity of involvement and joy of teaching maths..... I never seen in any teacher..🙏🙏🙏
A brilliant teacher, you should be teaching teachers Mr Woo.
Love it!!!!
I wonder if he would have made it easier for me on math - college level
you're a great teacher. Wish i had you instead of my maths teacher.
Note to Myself:
মধ্যবর্তী কোণ ↔ Included Angle
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.
yes that’s heron’s formula
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!!!
Yeah components i love those
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!
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.
These videos are awesome!
MIND BLOWN
Wish had teacher like this when i was in college learning geometry. Very neat and understandble because the way he explains things.
you explain the basics.good, good good..
He can exlain like everything so clearly
Explain but whatever
Every time I see your videos I fell like I want to become your student....
I feel like ime part of the class on a Sunday morning this is fun...
This has to do with the Law of Sines/Law of Cosines.
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”.
I think he's a teacher cause of students :)
I am also just like you I want every derivation
Actually not a rectangle but a parallelogram.
Please share your formula sheet.👨🎓
You are a great guy
That's awesome! Thank you!
Mi incantin lastenichon matenumereichon
Mi incantin lastenichon matenumereichon
Awesome maths teacher.
Good damm matgs are amazing
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?
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.
thank you sir😃
Lucky students
I wish I had him
do u do tuition
💕💕💕💕💕💕✌🏽
love you
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.
Wow...