Grade 10 MATH Term 1 Week 1: Solving Oblique Triangles - Laws of Sines Ambiguous Case | MATATAG - Q1

0:07 [bell] >> Hello everyone. Welcome to Math Easy YouTube channel where you can find free Tagalog mathematics tutorial. My name is teacher Van and tuturuan ko po kayo sa inyong mga math lessons. Our topic for today is all about law of sines and the ambiguous case. Don't worry. Step by step about law of sines and how to solve oblique triangles including the ambiguous case. Okay, so without further ado, let's now begin with our lesson. To start our lesson, let us have the review first. Okay, let me go over triangles. First, let's have the right triangles. I believe you already have learned the right triangles. And solving a right triangle

0:54 means finding the measurements of all the three angles and all three sides. Triangle ABC with angle A, B and C and sides A, B and C. So, how are we going to do that? Technique para ma-solve natin yung mga missing measurements. Okay, that is the trigonometric ratios. Meaning, we have the sine, the cosine and the tangent. Nemonics for nothing dito is yung so ka toa. Meaning, for so, sine is equal to opposite over the hypotenuse. Okay,

1:41 remember these parts of the right triangle. Next, cosine means adjacent over hypotenuse. And then for tangent, it's the opposite divided by the adjacent. So, it will be in solving right triangles. Now, oblique triangles? And what are we going to use? Nothing. For oblique triangle First, but you have nothing oblique triangle. It is a triangle that has no right angle. We have acute triangle. I got it to pull on each one of them. I think oblique triangle. All angles are less than 90°. So, for example, we have a triangle with measurement of 50°, 60°, and then 70°.

2:27 Now, these are all acute angles. Now, I also have the obtuse triangle, which means once one angle is greater than 90. One example of this triangle is this one. So, we have here an angle 30°, 110°, and then 40°. At least it is a total of angles that are all greater than 90. All right. In order to solve an oblique triangle, we need to know the three parts of which at least one is a side. para ma-solve nothing parts triangle. So, parts at least it is a side. Okay? So, we have combination of angles and sides. And how are we going to do that? We now

3:14 use the sign law and the cosine law. Okay? So, the law of triangle is para ma-solve nothing oblique triangles. But, for this lesson, we will just focus on sign law. Okay, what are the law of signs or you can nothing sign law? Okay, if we have here an oblique triangle with this uh uh illustration. We have here angle A, B, and C. Remember, uh you have opposite angle A is side A. Opposite angle B is side B. And opposite of angle C is side C. Now, we have this formula. Okay, so we have here A or side A over sine A or sine angle A is equal to B

4:01 over sine B equal to C over sine C. Now, aside from this form, we also have an alternative form, which is sine A over A is equal to sine B over B is equal to sine C over C. So, it will be not that then if we are solving for the angles. And it will not be usually not then if we are solving for a side. Okay, now, we have here three proportion pairs.

4:52 Here you can see so we can have A over sine A is equal to B over sine B. And another pair is B over sine B is equal to sine C. And then last pair can be A over sine A A is equal to sine C. In each one, there are four variables. And then four variables not then we have one, two, three, and four. If you know three of them, you can find the fourth. Okay? And Okay don't

5:40 Okay, now let's have the next part. Okay, should we use the law of sines? So, let's have this matching activity. Match each oblique triangle with the correct type of given information. So, remember there are different kinds of given information. It can be SSA, meaning side-side-angle. It can be side-angle-side, angle-angle-side, side-side-side, angle-side-angle. So, if you can still remember this, try to identify which among the uh uh uh numbers in the items done uh uh match as I think among choices if you want you can pause this video so you can answer and then review the different types of

6:25 given information in a triangle. All right. So, let's see the answers. Let's check. Okay, for number one, and about given information we have an angle-side-angle. Okay, so angle, included side, and an angle. For number two, this is an AAS or angle- angle and then we have here side. Okay, or should I do it uh counterclockwise angle-angle-side. Next, for number three, we have side-side-angle, side-side-angle. And then for number four, this is side- angle-side. And then lastly for number five, all of that are sides only. Okay, all of them angles. So, it is SSS. So,

7:13 there you go. I hope you got all of them correct. And this time, let me ask this question. Which of these triangles can be solved using the sine law? Okay, so try to guess which among them are uh uh uh we can use the sine law. Okay, so they are used for ASA, AAS, and SSA cases only. So, we cannot use the sine law for side-angle-side and side side side. So, I'm going to go get me nothing to do is the cosine law. But I don't know nothing to do is a solution that video. All right, so let's focus on solving oblique triangles using law of signs for

7:59 these cases with let's have angle angle side and then angle side angle cases. All right, let's have the first example. So, we have here solve the triangle shown in the figure. So, we have here triangle ABC. We don't have 40° angle and then 65° angle data. And then we have a given side. So, I don't know case it though. All right, yes this is the AAS case meaning two angles and a non-included side. So, we have here the two angles and then you 12 nothing to do is a non-included side because it's not between A and B. Included that is it to the side but what so it is called non-included side.

8:46 Now, let's identify the other parts. We have here A, have side B is unknown and side C is also unknown and then angle C is also unknown. Now, let us have step one meaning we will find the third angle first. So, one and nothing angle okay. Nothing to do is third angle given you one angle. So, we are going to use the concept of the sum of interior angle which is 180° minus the sum of these two angles which is A and B. Remember, the interior or the sum of interior angle of any triangle is equal

9:32 to 180°. So, we have here 40° angle A and then 65° for angle B. If we're going to add this, we will be having a 105. Okay? So, subtract nothing you own 105 from 180°. Therefore, we will get 75°. This is now the measure of angle C. Okay? 75°. All right, one down. Let's have the other parts, which is side B and then side C. That will now be step two, solving for side B and side C. So, to solve that, we will now be using the sign law. So, let me not get anything on sign law. So, we have here this formula.

10:22 Or is on Paris. So, we have here for B. Let's solve first side B. Okay, we can use A over sin A is equal to B over sin B. So, we can only use this pair. So, let us substitute first A. Our side A is equal to 12. Our side B is missing. Our sin A is a sin 40° because A is 40° and then sin B is uh sin 65

11:11 because B is 65°. Now that we have substituted all the given except for the missing, which is uh B, we can now cross multiply. missing or missing variable. So, we have here B. >> So, B times sin 40° is equal to multiply nothing to sin 65. So, 12 * sin 65. Okay, now how do we remove sin 40? We can divide both side by sin 40. So, we can cancel out your sin 40°.

11:58 40°. Now, this time how are we going to solve this? calculator's, okay? Okay, so any scientific calculator And then input nothing see 12 the numerator. And then our sin function and then press 65 close parenthesis and then the denominator input nothing see sin function 40° and then close parenthesis then press equal. Therefore our answer is 16.91957543. But usually

12:43 So, you have to ask them first. Therefore, our answer is B is approximately 16.92. It means approximately Okay, so again, our B is 16.92. This time, let's now proceed to side C. Okay, so to solve side C Yes, we are going to use A over sin A equals to C over sin C. Sir, question in solving for C can we use B over sin B instead of A over sin A? Actually pwede po kasi sagot na po

13:29 natin kanina 'yung side B and then given naman 'yung angle B, so we can actually use B over sine B dito. Okay? But for me, I do prefer kung ano 'yung original na given kasi mas sure po 'yun 'no. Kasi pag 'yung nasagot natin kanina, what if hindi tama 'yung ating sagot eh 'di 'yung sagot natin for this step is magiging mali na din. Okay? Now, let us substitute A is equal to 12 and then sine A is equal to sine 40°. Now, here we have sine 75 for angle C and then we can now proceed with the cross multiplication. So, C * sine 40 is equal to 12 * sine 75°. Okay? We can now divide both side by sine 40 para

14:15 ma-cancel out natin siya. Do'n din sa kabila. And then here, we can now proceed to our calculation. Let's use now our calculators. Okay, so C is approximately 18.03. Our side C is now 18.03. There you go. Na-solve na po natin lahat ng parts ng ating triangle, all the missing sides and the missing angle. Okay, let's have example number two. Okay, this time anong case po ito? So, this is the angle-side-angle case wherein we have two angles and an included side. So, we have again angle, side, and another angle. Now, ano po 'yung ating mga parts? Okay, let's label

15:01 them. We have here, this is side B opposite of angle B. And then we have here side A and side C and lastly our angle B. Okay, let's now have the first step. Okay, first step is to find the third angle. So, again, ang pinakauna nating hahanapin is 'yung missing angle. So, we have here two given angles. How do we get the third angle? We just use the sum of interior angle, 180 minus the sum of these two given angle. We have 50 plus 70, it will be 120. So, 180 minus 120, it will give us 60°. So, therefore, our angle B is 60°. Now, let's have step two. We will now

15:47 solve for side A and side C using our sine law again. Now, let's have side A okay? So, let's solve for A using our sine law. So, let's substitute side A is missing. Yeah, you angle A and you substitute nothing. And then we have here side B 15 over sine 60. Okay, which is angle B. You know you know what nothing can you know. Now, let's multiply this cross multiplication and it will give us A is equal to 15 times sine 50° over sine 60°. Okay, using our calculator press nothing you fraction. And then say

16:34 numerator input nothing see 15 sine 50° and then close parenthesis. And then say denominator input nothing see sine 60°. So, sine 60° and then press equal sign and our answer is 13.26827896 or approximately 13.27. Again, side A is approximately 13.27. Okay? Next, let's proceed to solving side C. Okay, so I don't care I don't care what you mean nothing to do. Okay, we can use B over sine B is equal to B

17:20 over sine B is equal to C over sine C. Okay, so here substitute nothing C B which is 15 and then C is missing. So angle B is 60 degrees and then angle C is 70 degrees. Okay, cross multiply nothing yet and then we can have C is equal to 15 sine 70 degrees over sine 60 degrees. Okay, let's press the fraction form input nothing C 15 times sine 70. Don't forget the close by calculator nothing. So the denominator is sine 60 degrees. Close parenthesis and let's now press

18:07 equal sign. The answer is 16.27595363 or approximately 16.28. Again, C is approximately 16.28. missing parts. That's how we solved the ASA case triangle. >> [music] [music] [bell] [music]

19:01 >> Okay, let's now proceed to the third case or the SSA case. Ambiguous case. Okay so ambiguous case. The ambiguous case So, it is the SSA case or two sides and an angle that is not included between the two sides. So, side-side-angle case. But what is the now what is the ambiguous case? Okay, let's have this figure for acute triangle. As you can see, we have here this triangle ABC with 32° angle. And then given for nothing is young side A, side B and then the angle A. So, I am that long young young boy young given. We don't know and measurement and C,

19:47 angle C and angle B. Aside from this, it can also be an obtuse triangle. So, I know you given the two it can be the side A and then side B and then the angle A. So, again in the pool nothing alarm and measurement and side C, angle C at young angle B. Now, why it is called ambiguous? ambiguous but now because nothing ambiguous the word ambiguous means in the pool share clear. Okay, why? SSA is ambiguous because the same given measurements may lead to three possibilities. That will put you on waiting my second nothing veto owner will not put down my mobile phone triangle given the conditions.

20:33 What else waiting is a the triangle and and then lastly waiting the lower case young possible making triangles but it to young given the parts known oblique triangle nothing. So, that is the meaning of ambiguous case. Okay, but I must maintain the young you let us explore using this demonstration. Okay, in this demonstration we are going to explore the SSA or the side-side-angle case of an oblique triangle. So, given this triangle ABC and then sides ABC, I make my cases And then a non-included angle. For example here

21:18 side A and then measurement side B and even the angle A. But for the rest, like for example angle C angle B and side C So how are we going to know if we can really form a triangle or none or even two distinct triangles. Using our altitude or young triangle. So how do we do that? Let us compare side A the length of side A with the length of the height of the triangle. Side A

22:07 Can we even form a triangle? Now what should be the measurement of side triangle. Okay, it can be no young side and adding a young measurement and a side A a altitude or height triangle. So triangle it sure is We now have here a right triangle. So it's triangle Now what if young side

22:53 Let's say height and then must my hobby then push or even side B. side B Yes, okay. We can actually form a triangle. So, as you can see or side B we can actually form a triangle. Okay, one triangle. Now, for the third condition, what if you triangle and I think side I must

23:38 altitude or side height side side side measurement number B Okay. or Hindi Okay, actually Yes. triangle. So, this is a triangle. Actually, I think it's a triangle. I think it's a triangle. So, aside from this triangle we can also create or form another triangle which is this one. So if our side A is longer than height but

24:29 shorter than the side B. ambiguous case Like for example, this one. wedding a triangle especially if our side A is longer than B and then the height we can form this one triangle or side A height one apple triangle >> Those are the cases for an acute oblique triangle. Okay, let's say an angle of the triangle

25:14 is more than 90. Okay? So, it's an obtuse triangle. Okay, as you can see, we now have here an oblique triangle. Okay, now, how can we be so sure that you given my Cabo triangle? So, what do you do you height? We don't need the altitude or the height. We just need to compare you side A and B doing the side B and given. Okay, so let us compare. What if you can side A or my stomach sick Kaisa some measurement none side B. Can we form a

26:01 triangle? Remember in the pool nothing wedding bag will be in your beginning obtuse angle. So, here we can only move the side A. Okay, so do we have a triangle? What was so there will be no triangle if side A is less than side B. What if or let's say equal to you can measurement my Cabo triangle. What will be so it is less than or equal to B, there's no triangle. So, if A is less than or equal to B, there will be no triangle. Now, what if A is longer than B? What if A is longer than B? As you can see, A is longer than

26:47 B my Cabo triangle. Yes, my Cabo in the pool and triangle can hit the none. difference. Okay? And much more triangle. So if we have here A is greater than B for an obtuse triangle, then there will be how many triangle? One. We cannot form any other triangle except for this triangle. So that's how we explore the ambiguous case of an oblique triangle. Okay, so it

27:32 ambiguous case conditions summary for ambiguous case for SSA let A is equal to the given angle A is equal to the side opposite angle A and B is equal to another given side. So for an acute angle, the conditions. So if A is less than H or the height, there will be no triangle. For A is equal to H, one triangle or one right triangle. And then if A is greater than the height, but less than the B or the side B, there will be two triangles. So you have to be careful with this case. Because the two will be the answer. And then for cases where A is greater than

28:21 or equal to B, Okay, now for obtuse triangle, the other conditions are here. You just need to compare A. If A is less than or equal to B, there will be no triangle. And if A is greater than B, there will be one triangle. Okay, so there are six conditions. >> Okay, now you might be asking how do I find H or you might think height. So to find height, we can actually use the so called toa. So by now you will be

29:07 on using the sign function. We can use opposite over hypotenuse. And remember, if we have here sign A our opposite is the height and then the hypotenuse will be side B. Therefore, sign A is equal to H over B. Okay? Now we have here B sign A is equal to H. Therefore, but it turn out then H is equal to B sign A. But I am going to put nothing is you H. For us to know the value of H, we just need to multiply side B times sign angle A. So again, it will be your

29:53 summary. Okay, in this part of our lesson, let's have more examples on how we solve ambiguous case triangles. So let's have the first one. Okay, determine if a triangle can be formed using these measures, then solve if possible. So if we have here angle A 45°, side A is 15 and then side B is First step is to check if it is really SSA case. So side side angle we can actually estimate. Label the parts.

30:39 Okay, so we have here angle A which is 45°. We have here side A, which is 15. We have side B, which is 10. And then, side C is unknown, even angle B check out your angle C nothing. So, is this really SSA? We have your side side angle. Yes, this is an SSA case of triangle. So, let's have step two. Compare nothing you. A side A check out your side B nothing. So, if we are going to compare A and B, so we have here A is equal to 15. And then we have B is 10. Therefore, A 15 is greater than 10. Okay, but going in for your acting case, we can say that there is one triangle. Okay, only one triangle is formed. Now,

31:26 for step three, we can now solve for that triangle. Okay, now in solving angle B and angle C, we can use the sign law. Okay? But, we are not going to use this form because it will usually get the government nothing to solve the non-side. But, rather we will be using the alternative form. So, which is you angles and nothing to us. Nothing numerator and then you sides nothing and nothing about. Nothing to focus it on the government when we are now solving for the angles. Okay, let's start with angle B. Okay, let us use this pair sign B over B is equal to sign A over A. So, let's substitute. Our side B is 10. Our side A is 15. Our angle A is 45. Let us

32:11 cross multiply and we will now have sign B is equal to 10 * sign 45° over or divided by 15. So, let us use our calculator by a computer to talk. Okay, so going in acting calculator press nothing you fraction and then input nothing see 10 times you acting sign function 45 close parenthesis and then the denominator is you 15 and then let's press equal sign. We can just press SD card. Okay, so nothing in my kitchen nothing in decimal form. So it is 0.4714045208.

33:04 final answer So you have to take note. sign which is Did you say calculator? You press the button you shift. And then click nothing see sign inverse sign so press nothing see sign. And then we will press answer. And then our close parenthesis. 0.47 And then click equal sign. final answer

33:50 28. 55057 but we can just round this off to 28. 1 Okay, so our final answer is 28. 1 degrees 28.1 degrees for angle B. Okay, now we are ready for angle C. Okay, for the third angle must be the dinner we now have two given angles and we are just going to look for the third one. Instead of using the sign law we can just use the interior or the sum of interior angles of a triangle. So C now is equal to 180° minus the sum of the given two angles,

34:36 which is 45 + 28.1, it's 73.1. So, C now subtract nothing in from 180, our answer is 106.9°. Okay? And lastly, for side C, you put your acting step four, we can use the sign law. So, you original or you acting on the form of sign law we can use this. So, let's substitute. We have 15 over sign 45° is equal to C over sign 106.9°. Our answer is 15 * sign 106.9° / sign 45. Okay, using our calculator we have 15 * sign 106 106.9

35:23 and then close parenthesis that was above we have here sign 45°. Equals it to that acting so good. We don't need to use the shift because we have nothing nothing to do is you side in the pool you angle. So, it's 20.29. I am so complete in the pool nothing sides and angles nothing triangle. Okay, let's have example number two. All right, so given this values, let's try to estimate or make an estimated drawing in the necessary not accurate in your drawing nothing. But I don't want to check nothing in your drawing nothing in acting triangle. So, we have here the the values are A is equal to five, B

36:10 is equal to 12, and then we have here angle A, angle B is missing and also angle C and even side C. So, you might questions nothing is is it SSA? So, as you can see we have here side side angle. So, this is yes, what else? Is it acute or obtuse? Okay, so since I'm acting given angle is 35 less than 90, so it is an acute triangle. Next question is is side A greater than side B? Hindi po siya greater sa side B. So, the answer is no. So, if you compare nothing can you know Hindi siya makakabuo ng isang triangle. Kailangan pa natin i-test para makita

36:57 natin kung ilang triangles ang mabubuo niya. Baka naman dalawa or wala talaga. So, the next step will be to find the height. Okay, so it will be the height nothing height test. So, how do we find the measurement of the height given the formula na binigay ko po kanina we have here H is equal to B times sine A. Let us substitute. We have here B is 12. Okay, and then we have here A angle A is 35 degrees. So, if you calculate if we try to input this and nothing is 6.88. So, our height is approximately 6.88. Now that we have the height, we can now compare you nothing side A to

37:42 height and then let's see greater by or less than. So, A is 5 and H is 6.88. Therefore, A is less than the height. So, since A is less than the height, no triangle can be formed. So, Hindi po tayo makakabuo ng triangle given this measurements. So, the actual illustration nothing is accurately. The actual illustration is like this. So, we have here 12 nothing side B and then you side A is just 5 and you side A is just 5. Makakabuo ng triangle. Hindi niya ma-reach you point B. Okay, so that's the second example for SSA case.

38:27 Okay, let's proceed to example number three. Okay, let's find out or Okay, so these are the following given. So, let's check the triangle. Let's estimate triangle. As you can see, greater than 90, so this is an obtuse triangle. So, estimate nothing you want parts now. We have here A is equal to 8 and then we have B is equal to 10. Okay, now before we go and solve the other missing parts. Nothing nothing you want questions like this. Is it SSA? We have side side angle. Yes, this is SSA. Next, is it acute or obtuse? Well, this is an obtuse triangle. Now, aside from those questions, nothing inspect

39:14 you triangle. Realistic quantity and it all B is 10. And then A is just 8. But when you know how long is side A? Is it really accurate but then it all triangle nothing. Is there something wrong? So, remember in any triangle if one angle is obtuse, the side opposite that angle must be the longest side. So, nothing obtuse angle. You opposite side you nothing how long is side. Is this the longest? In the middle of the 10 meters of the side B. So, if we're going to compare A and B, we can say that A is less than B. Since

40:01 A is less than B, there will be no triangle to be formed. So, this cannot be solved. So, the is it all triangle. So, A is just 8 and it will be able to nothing vertex in the portal triangle. Okay, so let's now have the last example for SSA case. Let's see if this given measures can form a triangle. So first step nothing is inspect or check nothing young triangle mag estimate let's just draw a simple triangle here. We have here ABC and then the angle a is given 40 degrees. I don't know given we have a is equal to 10 and then B is

40:47 equal to 12. Okay, now let's ask is it SSA? We have side side angle. Yes, and then next question is it acute or obtuse? The answer is acute. Now is a greater than B. Okay, once a is greater than B. There will be one triangle. Okay, so let us compare. It's a 10 and then B is 12 indeed. So it's less than B. So the answer is no. Then we can now proceed to the height test. Okay, find the height and compare it with a. The lower your acting triangle. So let's compare. Okay, so nothing you might we

41:32 have here H is equal to B sine a substitute nothing. B is 12 sine a is sine 40 degrees. Okay, if we use our calculator, we will have 7.71. Okay, so let's compare. Is a greater or less than H? We can see that a is greater than H. Okay, therefore if we're going to compare a b and H, since H is less than a and a is less than B. 7.71 is less than 10 and 10 is less than 12. We can say that there are two possible triangles. Okay, so the lower I think is to solve data. So, let's now proceed with the solution.

42:18 All right, let's solve the first you want to nothing triangle. So, here we have the first triangle. Since the level you want to move on nothing triangle data, must move up a bit cooler that again nothing none distinction you want to move on parts nothing. So, for example here you want to side see nothing. We can have C sub one because you want to move on my own power lead. Is that the triangle? So, if So, next is we have here uh uh angle B sub one. The real nothing alarm measurement. And also the angle C sub one. Okay? Now, let's proceed to solving the angle B sub one. Okay, so how are we going to do that? We will use the sign law. So, using the sign law, we have here

43:05 sign B sub one over B is equal to sign A over A substitute the long nothing you want to move given values. And then cross multiply nothing. We will have here sign B is equal to 12 sign 40 over 10. So, go ahead and do nothing calculator. Okay, press the long nothing you want to fraction sign and then we have here 12 times sign 40 close parenthesis that goes to the bar we have here 10. Press nothing on equal sign. Now, again this is not our answer. This is just the value of sign B. But I want to move on nothing you want to value nothing angle B. We will press shift and then you want to nothing sign but I want to move on nothing you want to inverse sign or you want to arc sign nothing and then

43:50 press answer. Close parenthesis. Equals. I want to move on nothing so good. It's 50.47. Okay or we can just round it up to 50.5. Okay, so again this is approximately 50.5 degrees. Okay, now let's solve for side C, okay, or C sub 1. Okay, so since we are going to angle B, let's now solve for side C using our sine law. But then we are going to see at A. So we have here C over sine C is equal to A over sine A. So let's substitute and let us cross multiply. Okay.

44:37 10 * sine 89 .5 close parenthesis over we have here sine 40 close parenthesis equals there you go 15.55. Okay, so again our side is 15.55. Now again it still depends on your teachers. If you are going to round off to the second decimal place then you follow their instructions. Okay, now let's proceed to side C where in we are going to angle A and therefore we are going to angle A and angle C. So we just subtract it from 180. So we have here 40 + 50.5

45:26 you will have 90.5 subtract it from 180 and we will get 89.5 degrees. Okay, so there you go. Now let's solve for angle A and angle C and angle B and side A and side B and side C. Now let us continue and let us solve the second triangle. Okay, for the second triangle as you can see we have here the first triangle if we are going to move the angle side A we are going to angle A and angle B and angle C and side A and side B and side C. So if we are going to make this bigger,

46:12 And then second is it to must my lead not triangle. So, let us get this part of the triangle. So, remember So, let us focus on this a smaller triangle or the second triangle so we can study this further. Okay, so here in the second triangle, you labels nothing to or sub two. Okay, to differentiate it from the first triangle. And let us identify you missing parts. So, we have here side C sub two and then we have here angle B sub two and then we have here the angle C. So, you is to solve nothing. So, using our triangle, nothing you angles nothing.

46:59 So, we have here angle B. Okay, we can use the clues from the other triangle. We know a while ago that this angle is 50.5 degrees. Okay? And we know that this is an isosceles triangle. You sides triangle I even you opposite angles in the They are also the same. So, if this is 50.5 degrees, this is also 50.5 degrees. And if we know that this is 50.5 degrees,

47:45 nothing you angle it to using the concept of what we call linear pair. Okay so angle B, we can now subtract this angle 50.5 from 180. Because you have a straight angle is 180°. Minus this pair, linear pair, we can now have the other pair which is 129.5. All right, that is now the value of our angle B sub two. Okay next. Okay, to solve for angle C sub two, since given that we are an angle that was given in this angle, we can now use the sum of interior

48:30 angles. So, 180 minus the sum of angle A and B, which is 40 plus 129.5 is 169.5. 180 minus 169.5 is equal to 10.5°. You know for you so cut an angle C. Okay? And lastly, is to solve the nothing new is young side C. Okay, or young C sub two. So, using our sign law, okay, C over sign C is equal to A over sign A. We can substitute. We have here sign 10.5. And then we have here 10 over sign 40. Cross multiply nothing and using our calculator, if we input this values, we will get

49:16 2.83. Okay, you know for you so cut nothing side C. Okay, there you go. Nothing for nothing young sides and angles young second triangle nothing. Okay? So, again, in our example number four, the young possible triangles and then the solve nothing young malaking triangle including young mas malit na triangle. So, again, triangle one at the point of my values the solve nothing and then triangle two at the point of my values the solve nothing. So, I hope nothing to do with you for I hope nothing to do with you young malaking process. Come here Joe and he put my shadow clear. You can always go back to the steps now. But in the same pool nothing can be now. Okay? All right. So, for our summary, okay, we

50:01 have learned the law of sines and it is used to solve oblique triangles when we have an opposite angle side pair. So, this is the law of sine wedding ballet terrain. As an alternative form. And then we can only use it for AAS AAS and side side angle. But we have to be careful with side side angle because this is what we call the ambiguous case. Okay, but it's for ambiguous case. It can have no triangle, one triangle or even two triangles. Two distinct distinct triangle. Okay? So, before we end our class discussion, okay, I have here an activity for you. You can answer this on your own. Try to apply you steps now and I forgot you did this at the end

50:47 video lesson. And then if you want to check this, you can check this with your teachers. Especially if your teachers are using our math easy PowerPoint presentations. Okay, but for now, thank you very much for listening. I hope now I intend to do your lesson. And so so so now I hope to see you again on the next video. But for now, bye-bye and God bless. Please click the subscribe button to support this channel. >> [music] [music]

51:32 >> God bless and [music] see you on the next video. Bye-bye.