RELAÇÕES MÉTRICAS NO TRIÂNGULO RETÂNGULO \Prof. Gis/

Take a look at the name of today's class content. Guys, look at the metric relations of the right triangle. Then I'll start the class by asking questions, do you know why it has that name?

Look here, right triangle, this is fine, right? Everyone knows, a right triangle is a triangle that has an angle of 90°, but now metric relationships, well, if you look here, metrics, metrics, it is related to measurements and relationships, so it means that there are relationships between measurements of the sides of a right-angled triangle. And then, see that I have already brought you a drawing of a triangle that is rectangular.

I'm going to show you there, because it's very easy to start this class by showing you what relationships exist between the sides of triangles, right? You come here, I write and you exercise without knowing where these relationships came from. So, for that reason, I'm going to explain in detail how I approach each relationship, okay?

So we're going to start by looking at that triangle there, the first one, triangle ABC, this triangle ABC is a right triangle at A, I left it to mark with you, because it has a right angle there at A, now what do we Do we know of a right triangle? I'm even going to get my ruler here. We know that a right-angled triangle is composed of legs and the hypotenuse and do you know what the hypotenuse is in this triangle ABC?

The hypotenuse is always the longest side of the triangle, isn't it? And the biggest side of the triangle is the one that's hard to look at. No, it's not, right?

You can also think that the hypotenuse is that side that is opposite the 90° angle. Oh, so here, the angle is here, here I have hypotenuse. So, if this side, this segment BC is the hypotenuse that is facing the vertex A, I'm going to call this hypotenuse azinho, okay, let's name it azinho, just to name it.

Now, this segment formed by BA and this segment by AC. What do we call it then? of legs so, I see that I have the side here, which is the segment AB and the side here, which is the segment AC, now let's also name it as we did with our hypotenuse.

As it was the side that was facing vertex A, I called it little cat, now this side, it is facing vertex C, so I will call it cezinho and this other side that is facing vertex B, we let's call it baby. Ah, but why am I giving the name? Because we are going to start building if it builds not visualizing the metric relationships, the relationships between the measurements of the sides of this triangle.

And what's more, when I'm working here on this triangle, it's possible to visualize the height of this triangle in relation to the hypotenuse. So I'm going to plot height by height. It comes here from vertex a until it reaches this opposite side and remembering that the height always forms a right angle with the side that with the opposite side.

In this case it would be hypotenuse. So look, I'm going to draw, I'm going to draw here for you the height that it comes from vertex A. Look here, look, and it arrives, then on the other side, on the opposite side, and what I told you even that at this height forms a right angle with the side, right?

So here I have a right angle. Look here how it turned out, so this size that I have here now, that we just drew, will be called h, because h is tall, but the height is like Gis, because you put h, because the height is there from English which is Hi, isn't that true? So then they use it with h, then we have other measurements that we put in this triangle too, which is the measurement that comes from here to C.

Ah, I forgot here I'm going to write that it is h, which is called the foot of height, okay? In relation to the hypotenuse, so this little letter is the segment and this h is the indication of this vertex here and now, guys, how can I think of these other measurements that I mentioned? So, if I think from h to c, from h to c, I'm going to come here and I'm going to call it M from M to B to H, I'm going to call it n?

But what are this N and this M, they are projections, okay? Projections of these sides B and C in relation to our hypotenuse, okay? So this side b here I have its projection that forms the M here.

The C projection forms the N in relation to the hypotenuse. So guys, I learned when I was studying, that it's like the shadow, OK? We have a light here, right?

Like there's a flashlight, production, where's the flashlight? Production, where's the flashlight, here's the flashlight, guys, get the flashlight, right? Who does it live, right?

Oh the flashlight, I learned it like this, I'm passing it on to you, but then the production started laughing, okay? If I put the flashlight here, it says it will make a shadow. So take this side here b, then it will be projected here, in this little piece it's good and if I put the flashlight here on side c, it will be projected here in this little piece called n.

Then the production team laughed, saying that they don't see any shadows there in the drawing I made, but guys, just so we can try to understand and memorize the projection, okay? So you saw that at the moment I did the height here, we managed to form the triangle ABC into 2 other triangles that are also rectangular, because see that we formed the triangle ABH which is here and the triangle AHC which is difficult to visualize there , huh? So look what I did for you, I brought the triangle here separately, so here it would be the blue one.

It would be the ABH triangle, okay, we're going to put it in this triangle, people down here are putting everything together. I'm going to put it in this other one so it's better to see what's here? Leave our, our little scribble there.

So here I managed to form this triangle, ABH, so what. I managed to form another triangle which is the AHC which is here, the AHC triangle is better for you to visualize, right? So let's put it right here so you can clearly see the 2 triangles formed on top of triangle ABC, ok?

And now, that means we have H here, I'm just going to leave it marked, we then have 3 triangles, okay, and these 3 triangles that we have, they are similar triangles, ok? Triangle ABC, which is the big one, ABH and AHC, are considered similar triangles, because they have equal internal angles, with the same measure, right? If you look carefully, look, let's take this yellow triangle here again, let's put it here on the side and here the blue triangle, look.

If you look closely now at this triangle, this one here is ABC with this blue, which would be our ABH with the yellow, the yellow is who AHCO really is, ok, well broken down for you to visualize. So these 3 triangles here are similar because of the interior angles. You see, there is no right angle, there is a right angle and there is the right angle.

Here, look, you see that I have a pink angle here, look, the measure of this angle, pink is here, like here, like here, why is it equal? Hey guys? Because these triangles that were formed here, they have the same angles here, look, look, you see this purple angle here, look, it is here and it is here in the formation of the triangle.

It is good? So now we are going to relate the measurements of these 3 triangles that we formed, because then we can find what the relationships, metrics, are. So let's call this triangle here triangle, 1 this one triangle 2 and this one triangle 3, but let's put the little names so we can look better.

Then make the connections. So here I'm going to take it from here and move it over here. This is the same one, okay?

I'm just not going to stay here because it's too scribbled. So, oh hypotenuse, which is A here. I have side B, let me delete this one here, oh side, B and here would be our side C, so this is our triangle, great.

Here's what I have, but I'll have to delete 2 also in production. I wrote above what do I have right here? What is this measurement?

If I look at the triangle, it didn't come from here, look. It didn't come from here, so this measurement is side C, which came from there, so let's say that here is measurement c here, who is this measurement here, guys? This measurement would be the measurement h that comes from the height, remember, right?

It came from above, its formation here, look, and this tiny measurement here is the projection, it's the N projection, so here is the right n, now the triangle 3, which will also have to be erased here, let's go for more here, so you can see it better. A o H o C, so see that here I have leg b, that's because he was here, right? So this part here is b here is oh also, because it gives height and see that down here he is who our projection M, look what I have now, people.

Everything is drawn correctly for you to visualize the relationships, so we are now going to make comparisons of these triangles that are similar, so see that I am going to start comparing triangle 1 with triangle 2. Okay, as they are similar triangles, the sides are proportional. So, if I look here, this side here which is side b, so let's start by saying here b is towards b this side here which is B is facing the purple angle.

Who is he for here in our triangle 2? who is facing the purple angle? Oh, whoever is facing the purple angle is oh, because I have to think that the corresponding sides are proportional.

I can't match this side here with this side here, okay? I have to get the corresponding ones so I'm going to look at the angles, the purple angle, facing the purple angle, is the B, purple angle facing the purple angle h so, the B is to h, just like, just like the that now I can think. Side C or C is for who in this triangle, people?

OC is not facing the pink angle, whoever is facing the pink angle, in triangle 2 there is N here, so C is facing n. Just like now, I need to relate the A, the A which is our hypotenuse that is facing the right angle. For those of you here who are left with the C that is facing our right angle, right?

So I did, I established a relationship between one, no, right? 3 relationships here of proportionalities between triangle 1 and triangle 2. Now we are going to establish the relationship between triangle 1 and triangle 3 and then we are going to make the necessary calculations, okay?

Now let's go, so here we are going to mark it, folks, that here I'm talking about triangle 1, I'm relating 1 to 2 to prove that you don't get lost, now I'm going to relate one to 3, okay? Then we do the calculations, calm down, let's just relate first, so, looking at 1 again, starting with B, side b of triangle 1 is for those in triangle 3, oh, this is b, which is also not that, he is facing the purple angle, no, B is facing the purple angle in triangle 3 who is facing the purple angle? It's M o, so b is for m, just like who else can I relate to now that they're proportional?

corresponding sides. OC, the C that is facing the pink angle, is for who here is facing the pink angle, so this side c is proportional to who here in this triangle? Now, guys?

In 3 who is facing the pink angle is, oh, so C is to h, just like? Now relating the hypotenuse, which is proportional to the hypotenuse in triangle 3. So that means that here I have the is so where is the hypotenuse?

The hypotenuse is here facing the hypotenuse. I have B. OK, so here I related 1 and 3.

Don't worry, there is no relationship ready yet. I'm just writing so you can understand. So what are we going to set up now?

Now we're going to look at triangle 2 and 3, we mark 2 and 3 right there, so let's go there now. This one with this one. Who are the proportional sides?

Remembering that they have to be corresponding. Let's start here. OC so side C is to whom people in triangle 3 is proportional, to whom?

C is facing the hypotenuse, so it can only be B, which is facing the hypotenuse here, so how can I write it now? ON could be the N, it doesn't matter if you wanted to start with the h, that's a problem, the N then the N is for the is different for the pink angle. Who is facing the pink angle here?

Look here. oh, so n is for H and finally, who was missing from relating now? ON is for H, now the H, the H, is for oh, is facing the purple in the yellow triangle.

Whoever is facing the purple or M, then see that I set up these proportions here now and from each, each of these proportions that I related, each 2 triangles, we will find the metric relations. You marked this well so we can form these relationships now. Let's go then.

Well, let's continue now, so we can carry out the metric relations that we have done so far, the assembly of these relations and do you remember that I said that the triangles were similar? Because I really want to see who paid attention, Why did I have similar triangles, because I had equal internal angles, right ? With the same measurement and proportional corresponding sides, make sure it has to have the corresponding word, because you saw at that time when I was looking at the drawing of the triangle I looked, Ah, this side here is facing the purple angle, so In the other triangle, who is facing the purple angle?

Because I had to look at correspondence, okay? That's why they have to be corresponding, because then they are, they're similar, right, guys? That's a good mark there, so let's go, enough talking and let's establish here now the calculation of these proportions so we can finally find what the relationships, metrics are, but let me say something now.

What I'm doing here is to show you how to arrive at these metric relationships, because as I said at the beginning, it's very easy to come and say, hey guys, these are the metric relationships, apply them to the exercises I learned So, my teacher showed me what the metric relationships were and I applied them to the exercise, but I didn't know where the metric relationships came from, so that's why I'm making a point of showing you how these relationships are formed. , which is based on the similarity of triangles, okay? So don't leave class and won't stay until the end to accompany Gis.

So let's go here, when I go to calculate the proportions, I have 3 there, right? 3 reasons 1 2 3. So I will always do 2 by 2.

First I start this one with this one then I do this one with this one and this one with this one, but I'll write it straight for you, so here the first one is cross-multiplying to calculate proportion, so B times n will be equal to CH, so look. CH, Ah, but is it okay to change the order I mentioned first BN? But I started from here, it won't be a problem.

Then. CH, is equal to BN ready. I've already made a metric relationship, now the other, so I'm going to start now with this first one here which is the B to h is for the last one which is the AC, so now multiplying the cross again.

What will I find now? OA times h is equal to BC, oh, cross multiply. If you want to indicate the multiplication between the 2 letters, you can do so.

It'll be the same too. And now, what do I really have to compare this one to, right? o C so, now I'm going to compare CN o CN with AC.

Cross-multiply, what will happen? Cross multiplying here, we will get c times. C which gives c squared and here will be AN wow, my n looks like an h my God, let me fix it here my n looks like an h it will be the same as AN this one is an n this production is not an h no .

My God, look N here, look, okay, so see that I've already managed to find 1 2 3 metric relationships and let's continue here now. When I compared 1 and 3, triangle 1 and 3 do cross multiplication. It will now be here, BH equals MC or CM however you want to put it, okay?

So who do I have to compare now? The first is the BM. I compare it to the last AB.

Cross multiplying will be b times b, gives b squared and M times a will be AM or MA however you want to write it. And who else do I have to compare now, let me see this one, which is our CH. Same as AB, like AB.

So doing the cross multiplication again, what are we going to find here now? Sometimes h is. Same as ABC, which is CB, whatever.

Then, look, you'll start to notice that you'll start repeating it, right? Do you see that this one is already here, look? So we will only compare, count only once, when performing the total count, now continuing with the last one.

Phew, right guys, so much. You already know how to do this one by heart, Huh, c times h so go there c times, h is equal to BN, there's no longer that one here either, where's the CH the CH is here, oh CH the same BN, then it's on, it's just repeating the count once later. Now I'm going to do the C is to b with oh to m cross multiplying, which we're going to find that we're going to have now the Ah, I'm going to start from BH to be the same as the others BH is equal to CM, which is fine, I I know you're going to repeat it, where is it, here, repeating it again and finally I'm going to compare N with H, NH with HM.

And multiplying these 2 here. Now, what am I going to find h times h= H squared and then m times n or n times M however you want to write it, why am I going sometimes, don't you need to? MN or NM, guys, now let's highlight those that we found that are not, oh the one I have a metric relationship, oh one here, 2 is 2, which one else?

This one hasn't repeated yet. So I have 3 here, the third. The fourth metric relationship Oh, my God, how big did that get?

This one has already appeared, right? It's here, so I won't highlight it again. Are there any others that have already appeared?

CH, CH already appeared there, so I won't highlight BH already appeared here, so in the emphasis and this one, oh BH squared is equal to MN, so H squared MN, B squared equals AM but I left one behind, Guys, I was already going to suspect this one was missing. Which was C squared equals AN. So we highlight, o 1 2 3 4 5 6 metric relationships that we were able to establish here.

Between the measurements of the triangles of the sides, of the triangles, right? Now I'm going to ask you a question, are you missing one? Isn't it sometimes like this, Oh, there's no need to say that, we already know, because every time we work with a right-angled triangle, what do we really have in a right-angled triangle?

Guys, we have the Pythagorean theorem, don't we? Where is the right triangle, if you look at that here, look. It's a right triangle, isn't it?

So, the side that was facing the right angle, the big one, I'm considering the big triangle, the side here was the hypotenuse. Here it wasn't the cateta that was in the catheta ready, format a right triangle, Pythagoras' theorem, who remembers the Pittágoras theorem? What was it for us to write here to complete our relationships?

It was leg squared, plus leg squared, equal to hypotenuse squared. Pythagoras theorem and guys, now one more thing, I want you to look at the triangle, let me take it again. I sent it there, I'll get it again, look, one more observation that here is not a metric relationship, but it's kind of an obvious thing, right?

You see here, look, this is not the hypotenuse, because it is no different for the right angle, a wants the A that we called there at the beginning, you see that I can find the value of this a by adding the projection n with the projection m, so also if you want to mark that. Huh? You can mark that A, which is the total here, will be equal to N plus m is also something that we can mark to help solve the exercises later, so let's mark one more here, look, if I take it, then I add the M with n, which is the 2 projections, I get the value of the hypotenuse, I get the hypotenuse ready, guys, so much for you to memorize, but hey, this is obvious, right?

We can now look around and find out. But Pythagoras here already learned it a long time ago, right? You already know, right?

Pythagoras, also by Pythagoras, there are the others for you to memorize and then we will now use these metric relationships to solve the exercises. But then how am I going to solve the exercises? Ah, you have to know this, right, guys?

Which one can I use in that respective exercise? So now I'm going to help you understand this. Let's go then, guys, before doing the exercises I mentioned, I want to show you something.

That it is possible to arrive here at the Pythagorean theorem, in this relation by taking 2 other relations here, so, if I take this one here and this one here, look what I'm going to do, I'm going to take these 2 and I'm going to add them, then I I'm going to show you that you can get to the Pythagorean theorem, look, so it's like this, C squared equal to AN is not that, then I'm going to add it with this one here which is b squared with AM which is there. Let's add these 2 relationships here, what will happen? When am I going to join C squared with b squared?

What does your square with b squared give you? Well, as they are not similar terms, you can't put them together, so you can write that it will be b squared plus c squared, o this with this o. I just put it here in order, in no order for you, but it's the same thing, now let's add these 2 AN plus AM, I added these 2 and these 2 and if you wrote what to write in order, let's put it in order, so it's there, C squared plus B squared, ready.

Production is ready the way you wanted. And now, what do I do? Well, guys, now, let me write by changing the order here, you can write, right?

B squared plus c squared equals, do you see here that we can perform a factorization, common factor by evidence, do you see that A is common here? And A is common here, so I'm going to put the A outside the relatives and then I'm going to open it. Parenthesis, what happens now sometimes, when comes back in this AN?

Is it n itself because sometimes n returns to AN times how much returns to AN? Who knows? But it's m itself, right, sometimes m comes back in AM wow, but why did I write all this?

And now, calm down, you will notice b squared plus c squared will be equal to A Sometimes, people remember that I picked up the red triangle at that time and said, look, there is something that is obvious that we realize that if I then take and add the M with N which I find, even if I add the M with n from here it gives the value of a which is from the hypotenuse and one more thing, now that you observe, what gives A multiplied by A same people? Maybe b squared, but c squared will give A times A of A squared that I found here, guys? I managed to show you that from the combination of these 2 metric relations, we were able to find the Pythagorean theorem.

Look here, guys, mark this well too, which is very interesting, it's good, we already knew Pythagoras' theme, right, which looks at a right-angled triangle, we already remember it automatically in the theorem, but you can also do the his training here, right? Now let's exercise. So, in this first exercise, look, find the value of the unknown in each triangle.

Oh, our little column is already here for us to memorize to see which one we are going to use, so look here at this triangle, which is a rectangle that needed to be drawn here for us. Wow, it's designed now, guys, who should I start? Which of these relations am I going to use to find the unknown value?

I have to find out who is the value of H and who is the value of a ? ? Well, to find out the value of A, I'm going to tell you that it's easy, why is it easy?

It's not a right triangle, you can apply Pythagoras' theorem, I have a side, I have a side, I find the hypotenuse. Let's start then, using Pythagoras' theorem here, oh, so it's going to be b squared, plus c squared equals A squared, okay? Whoever is B can say that this is it, so it will be 12 squared plus C which is 16 squared.

This will give the value of the square. 12 squared is nothing less than 144, because it is 12 × 12 plus. 16 squared, which is 16 × 16, will be 256 equal to A squared, well, adding 144 to 256, we arrive at 400, 400 is equal to A squared.

How do I find the value of the number that squares it to 400. So in this case, what does it do? Just take the square root of 400, right, guys?

And the square root of 400 is 20. So, I can now find out that the value of a is 20. Okay, I've already discovered an unknown that I was looking for here, look, it's equal to 20.

Well, now I need to find out who is the h. Let's analyze these relationships that I have here. Which ones do you have oh, well, do you have, oh, do you have this one oh do you have this one do you have oh do you have this oh this one oh this one oh this one oh this one oh this one oh right, but now so I know which ones I'm going to use, since I have several, I have to think I only have it here for me to work?

The b side is what we called here B and the C side, now the A that I found then. What to think about which of these relationships? How about h but which is or b, or c or a because, look, if I start with this one, can I use this one?

CH, equal to BN, can I use this metric relationship? Even though there is h there, it's not true, because I don't have the value of n here, it's not marked, why would I want to find out if it's not needed here, ok? And it’s not even possible to do it, okay?

So this one is outside this one, Ah, it's the same as BC. Can it be used? I have the value of A, OK, I don't have h that I want to find out I have the value of b I have the value of c, so we can use that one, look at another one, which one else had this one, oh, why couldn't this one be used because there was an m here and I don't have the value of m in my triangle, that projection I don't have is outside and this one here, why can't this one be used because I don't have either M or N?

So the only one left here I can use, it will be A, A times h is equal to BC. So I can do this. Who is A ?

it's going to be 20 h equals 12 × 16, let's do the calculation here, because off the top of my head 12 × 16. 6 × 2= 12 goes 1, 6 × 1= 6, 7. 1 × 2= 2, 1 × 1= 1.

It's going to be 192 it's going to be 192. The multiplication here. How do I finish this calculation right now?

I do that h will be equal to the 20 that I was multiplying, it will be divided, so it will be 192 divided by 20, you can do 192 ÷ 2 and then divided by 10, add a comma. So, oh 192 ÷ 20, oh, I'm going to take advantage of the same content. It will be 9 because 9 × 20, there are 180 then 180 to 192, doing the short method, there are 12 left OK, 12 does not divide 20.

Then I come here and put the comma and the zero 120 to 20 are 6 with the remainder zero . So here, notice that I did the division here thinking about the short process? Why did I make the short?

Because there was little space, right, guys? It's nothing for us to practice either, right? So that means that the value of h will be 9.

6 and the value of a that we found was 20. So, can you put it here? H measures 9.

6, as he didn't give me the unit of measurement, if it's me or centimeter decimeter he leaves me without, right? For now, leave it as important as we can find it, so take a look at the exercise and now I want you to think about how I'm going to look at the exercise and find out which of the metric relationships that I'm going to use, I have to think about what unknown and I have to find out which one did you see that here is from h? I had it in several cases, but I was only able to use it in one, so you'll have to do it in the exercises you have there and I'll solve one more.

Guys, now that I need to find out the value of X and h, what am I going to do, which one am I going to use? There is no x here in my metric relations, well folks, this x is in the place of which of our values ​​here, of which letter of ours it is in the place of which one , analyze here with me, remember the triangle from the first class, I had placed, so there was A , B and C. That was not what we had placed, production was changed, this end was over here, there will be problems, people.

So let's say, if I put a vertex a here, I will have the azinho, right? If here I place the vertex b here I will have the baby if here I place the vertex c here I will have the cezinho in the same ways. Everything will be fine if you put the B here and the C here, you can be sure it will work.

And now? Well, if this is B, who is the X here for me? Is that the X that represents the M?

M wasn't that and here I would have N, but you don't need to find out where it's marked there, it's not asking because the statement asked, find the value of the unknown. Well, then let's start by finding out who this M is, so see that to find out M which of them here brings M to me several, right guys? So here I have M, well here I have M, but then I have A, OK I already have A but I have n there is no value of n people so we can't use this one plus this one here h squared MN, well, I don't have the value of h, I can't start with Ela and I don't have the value of n either, this one here b squared equals AM I have the value of b which would be 20 o M and A I have the value too We are about to put this one down, so let's start with this one so b squared = AM the AM has to change it makes a difference, no problem, but let's change it and continue as it is there.

AM will result in the same multiplication, because the order of the factors does not change the product. What's going to happen here now? B, B is not worth 20, so it will be 20 squared equal to the value of a which is 25, 25 m, right?

Because I have no value of m, which is who I want to discover, So just remembering that I used this metric relationship here to solve this exercise. Now squared there are 400, equal to 25 m. How do I finish an exercise like this?

This m that is multiplying here with 25 this 20 m, not this 25 that is here multiplying with m is dividing so what do I need to do now? 400 ÷ 25 let's put together the content here, look at 400:25, look. So, if I take 40 here, it is once 1 × 25, there are 25 and there are 15 left below this zero, oh 150, there are 6 times 25 which gives 150 with the remainder zero.

So this means that the value of our m will be 16 and now you have seen that there is a measurement unit that is in centimeters, so our m will be worth 16 centimeters. Guys, look at something here. Now if the M here that I just discovered is worth 16.

You can now find the N there, right? Even though you are not asking for the value of n, but you can think about it, to practice, how much N has to be, can you think here everything about e 25 if here it is already 16, how much is left to complete, to find 25 there are 9, so here our N would be 9, that's it, I managed to find out, right? I didn't need to, but I figured it out.

Now I need to find out who it is oh, guys, how do I find out who it is? Oh, now let's go again, analyzing who can we use? Oh, here I have h here I have h here I have h, here I have h all of them I have h, so, which one can I start with?

Could you start with this one since I have the value of c here? I don't have the value of C unless you want to find out the value of c by applying the Pythagorean theorem, look, because there's a right triangle, it can be done, isn't there an easier one, right? Sometimes h I need the HBC, I need the c here too, we'll give this one to start with.

This one doesn't have h, this one will also have the C which I don't have either. So skip it, wo n't there be any? I'm going to have to find out c first this one, oh h squared is equal to MN, I have m I have n that I just found N by accident so I can use that one there folks, because if I want to use it, use the others I I can, but to use the others I first need to discover this side and you can do that too, but as I already have it ready, I'm going to do the one I already have ready, so I'm going to start with the metric relationship H squared equals MN , oh, even emphasize here that I'm starting with this one, okay?

So, here I started the exercise with this and here I did it with this metric relationship, as it will now be in place of h, As I don't have it start with h squared. Just like AM, who is M? OM was 16 times N, N is 9, then h squared will be equal to 16 × 9, 16 × 9 is 144.

Now, what number do you square, which gives 144 and take the square root of 144. And what is the square root of 144? There are 12 people.

So does this mean that the value of h in this question will be 12 cm? The h, it's good, so let's come here and put it here, oh, it's worth 12 here for you, oh 12, oh. 12 cm.

Then I managed to solve the exercise and also, if you wanted to find out the value of being applied, we will have from Pythagoras squared side to is side squared, but side squared , is equal to the hypotenuse squared. Then you find out the value of c and then you would have all the measurements, but exercise is asking me, right, guys? We're just going to do what he asked, okay?

So leave it marked in your notebook so you can then practice the exercises you have there to ace them all. People mark these metric relationships and do what I did. Which one can you use?

Do it 1 by 1 so you can memorize it, okay? And then, share this class with your colleague, with your entire class, so everyone can enjoy the teacher's activities. It's OK?

Then everyone is happy and I'm also happy with that comment you're going to leave in class for me, thumbs up for you, I didn't ask today, subscribe to Gis's channel, if you're not already subscribed and leave yours like for today's class, which was super cool, today's class I showed you how we find the metric relationships of the right triangle, and I'll see you in the next class. Goodbye. .

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