[Music] in this video we're going to cover how we can use pythagoras's theorem to calculate the missing length of a triangle like in this one here where we're trying to find the length of x now the first thing we need to look at is which questions you should actually use pythagoras for in the first place first we need to be looking at a right angle triangle so if the triangle doesn't have a 90 degree angle like this one then we can't use pythagoras to solve it and we'd have to use some other method you also need to know the lengths of two of the sides it doesn't matter which two you know but you do have to know two of them like in this one where we know the length of three and four and lastly there has to be one missing length that we're trying to find so x in this case the equation for pythagoras theorem is that a squared plus b squared equals c squared and it's really important that you memorize this equation because it comes up quite a lot letters a b and c refer to the three sides of a triangle c is always the longest side of the triangle which we call the hypotenuse and it will always be opposite the right angle we've labeled c the other two sides will always be a and b and it doesn't matter which way round you put them so we could have a on the left and b on the top like we have here or we could swap them over it doesn't really matter as long as we have c as our hypotenuse and the other two sides are a and b then we're fine to use the equation all we need to do is plug the numbers that are corresponding to each letter into the equation so because a is four and b is three we'd write four squared plus three squared equals c squared and to work out what c is all we need to do is solve it like we would with any other equation in maths so we can simplify it to 16 plus 9 equals c squared and then 25 equals c squared and to get c by itself we just need to square root both sides which leaves us with five equals c so the length of x must be five have a go at doing the same thing for this question so again we're trying to work out the length of an unknown side x just like before the first step is to label our sides so a b and c and in this case the unknown side is c because that's our longest length next we need to write out our equation so a squared plus b squared equals c squared and then we can plug in our values from the triangle so 1.7 squared plus 3.2 squared equals c squared or instead of writing c squared we could put x squared because we're trying to work out x so that's effectively c in this equation then the final step is to solve the equation a question like this will normally be a calculator paper so the best thing to do is put the whole 1.7 squared plus 3.2 squared into the calculator in one go which gives us 13.13 which has to equal x squared so to find x we need to square root both sides which the three significant figures like asked for in the question would be 3.62 so the length of our missing side is 3.62 centimeters now one thing to point out which can sometimes be a bit confusing is that most examined questions will label the corners for you like they have in this one and when they refer to a line they use the corners it's connected to so when they ask us to find the length of x z they are asking us to find this unknown side between x and z so we could put a question mark on this side because this is the one that we're trying to find because we're going to have to use pythagoras theorem though we want to label our sides a b and c using the rules that we've already been talking about so from this point we can pretty much ignore the x y and z so we write out our equation a squared plus b squared equals c squared and plug in the values so 5.6 squared plus 10.5 squared equals c squared which if you put it into the calculator simplifies to 141.61 equals c squared and if we square root both sides we find that c is equal to 11.9 and so the length of xz is 11.9 centimeters let's try one more in this style so in this question we're trying to find the length of ac which is this one so we can give this line a question mark and from this point onwards we can ignore the letters that they've given the corners so we need to label our sides a b and c like we would for any pythagoras question and write out the equation a squared plus b squared equals c squared so that would mean that 8 squared plus 11 squared equals c squared which simplifies to 64 plus 121 equals c squared or 185 equals c squared and if we square root both sides that gives us 13.6 equals c and so we can write our answer as 13.6 centimeters anyway that's everything for this video so hope you enjoyed it please do give us a like and subscribe and remember to check out our website by clicking on the link in the top right corner of this screen and we'll see you again soon