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.
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!!
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.
"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!!
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.
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 !
@@rubikscuber1114 Aye!! This is my other TH-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.
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.
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.
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
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?
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....
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.
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?
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)
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.
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.
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.
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.
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.
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.
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.
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.
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.
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 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 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
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.
Even i am a graduated engineer, i enjoy and actually learn basic principles and logic of math from your videos. Keep teaching!
I already know this, but I still love watching your videos. It's so entertaining.
same
"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
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.
wow!!!
never knew that ½absinC could be proved that easily~
i just kinda take it for granted
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 !
The intensity of involvement and joy of teaching maths..... I never seen in any teacher..🙏🙏🙏
Thanks again Mr Woo, Math never fails to disappoint!
*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
Thank you
For recording all these amazing lessons
You'r the best teacher ever🌟
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 TH-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....
These videos are awesome!
Wish had teacher like this when i was in college learning geometry. Very neat and understandble because the way he explains things.
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.
A brilliant teacher, you should be teaching teachers Mr Woo.
That's awesome! Thank you!
you're a great teacher. Wish i had you instead of my maths teacher.
Love it!!!!
You are an incredible teacher... Its really nice to watch ur way of teaching.
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!!!
Thanks sir it helped me a lot. Your explanation was too good.
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
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....?
I did the Intermediate Maths Olympiad last Thursday, and one of the questions required this formula. I forgot the factor of 1/2 D;
You are a great guy
you explain the basics.good, good good..
MIND BLOWN
I see triangles and an eye....
David Robinson illuminati!!!!!
iloominati konfirmed ! LMAO
shat
Savage...
u have good sense bruh
Awesome maths teacher.
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.
He can exlain like everything so clearly
Explain but whatever
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.
over HEAAA
Sakman Nakki
*NAO OVA HEIA*
I wish i had a teacher like you when i was in school
Very good explanation
I feel like ime part of the class on a Sunday morning this is fun...
if i had to have anyone teach me maths this guy would do the job perfectly
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
Naaaahhhhhh my mind is blown😮🔥🔥
epic video
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?
Me: randomly learning math on Sunday because of how fun these videos are
You are a genius 😍😍
Yeah components i love those
Every time I see your videos I fell like I want to become your student....
Can I grab a copy of your formula sheet badly needed :
What standard is it?
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.
what grade are those kids from!?
wow i learned so much in few minute thank you sir
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?
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....
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
Don't need to go to math class, just see this guy videos
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.
Hey sir , I am from India and I am biggest fan of your teaching ,😊😊🙈
how do u know the value of the angle C
Good damm matgs are amazing
This is amazing, can I have the pdf of the formula sheet? It will help me ❤️
what grade is this?
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.
I have no idea what you are saying but I'm engaged the whole time
I wonder if he would have made it easier for me on math - college level
Thank you Eddi, your videos are helpful, however, I prefer the explanation to be always on the big whiteboard
do u do tuition
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)
Use herons formula
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.
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
Great
Which grade he teaches 😯😯
Rishi Raj all of them
Really a Richard Feyman in mathematics....
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.
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.
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
I wish I had him
thank you sir😃
what college/university is this, the lecture hall is sort of very small
This is secondary school, not university - it's a classroom, not a lecture hall.
This has to do with the Law of Sines/Law of Cosines.
Where am I?
Eddie Who is my hero. 🤓
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.
love you
I want to know how will you calculate sin c if it has any random value say 24? Any help would be great
Use a calculator 😂
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.
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
Where can I download your formula sheet summary? Thank you 😊
800k followers and no adverts. Wow
Hey there,
Tan C = h/b
h= b×tan C
If c --> π/2
What happens to h and a in Eddie's triangle
Than the triangle would become a line, as pi/2 radians is 180 degrees, the sum of all angles in a triangle.
Can u teach me everything plz
Just watch em vids! :D though you probably already have :)
i can't see your mic but the sound is ok.. the white board is too low, claim compensation for bodily injuries...
You only replaced an unknown value, h, by another unknown Sin C.
Please share your formula sheet.👨🎓
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.
Wow...