hi guys it's me teacher in our today's video we will talk about how to solve the missing part of a given right triangle using the so Ka and TOA so without further Ado let's do this topic so what we have here are the two examples that we have for this video and what we have here is to solve for the missing part of each right triangle using the so Ka and TOA before we dive in with this first and second example let's have the saw so stands for the sign is equal to opposite over the hypotenuse K it stands for the cosine is equal to adjacent side over the hypotenuse side TOA it stands for the tangent is equal to opposite over the adjacent so let's go with the first example this one is a given right triangle and what we have here is an acute angle which is the 36° so what we need to do here is to know what kind of side is this and this with respect to your acute angle 36° with respect to your acute angle 36° this side or the missing side which is X this one is your opposite side because that is opposite to your acute angle and definitely this side which measure Mees 10 cm is your hypotenuse because this 10 cm or this side is opposite to your right angle so what we do what do we need to do here is to list down what we have first we have the given which is the hypotenuse and missing or the missing part is the opposite side so how we going to decide which one among this three is useful for our given problem so remember you need to know which ratio has the opposite hypotenuse or hypotenuse in opposite okay very good you're correct we can use the so therefore we will use sign and then what we need to do is to copy the acute angle which is 36° so what we have is sin 36° and remember our ratio opposite over the hypotenuse we will substitute the value of the opposite side which is this is X and the hypotenuse is 10 copy this one we have sin 36° so what's next is we will cross multiply Let's cross multiply and then I will use a different ink I will cross multiply 1 * X and then 10 * sin 36 let's multiply 1 * X is X on the other side we have 10 * sin 36° so to get the value of this x we will use the calculator so to simplify this what you need to do is to input first 10 we will input first 10 and then press s 36 so even though press degree symbol or you can simply close it and then press equal sign so as you can see we have here 5.87 785 so to for our answer we will just have a one decimal place or decimal point for this final answer so if this is 5.87 785 and this is to be rounded off as 5.9 and don't forget the unit and that is ctim this is the length of our opposite side or the variable X now let's continue you with problem number two for problem number two so this is your right triangle and this is the missing side and this is the given side with respect to your 40° angle this x is the opposite and with respect to your acute angle 40° this is the adjacent side so what we need to do is to think which ratio has the opposite and adjacent okay very good we will use the TOA but before that let's list down all the given given is the adjacent side missing or what's missing in this problem is the opposite side we will use TOA or the tangent ratio that is tangent 40° and then capy the ratio opposite over the adjacent side this is tangent 40° is equal to your opposite side which is X over The adjacent side which is six okay so what we need to do is to cross multiply again I will put an invisible one here for us to multiply this x variable we have here and this one okay let's multiply this is 1 * X that is X for this copy 6 * tangent 40° now again we will use our calculators scientific calculator again this is very important press six then press tangent 40° and as you can see this is the answer so we have 5469 7787 so I told you earlier that we only have uh we will only express our final answer in single decimal but since this is zero and when we round it off it is a whole number final answer are here your X is equal to 5 cm and this is the answer for this problem guys so I hope guys you learned something from this video on how to find the missing sides or the missing side of a given right triangle using the sooka and TOA and as part of her routine I will give you this problem I will draw a right triangle and I hope comment section what is your answer answer in this problem so I will draw Pro right triangle here this one so the given R this is 34° this is 12 CM and the missing side is this so what is the answer so again guys if you're new to my channel don't forget to like And subscribe but hit Bell button for you to be updated set latest uploads again it's meon bye-bye