In this video, we're going to cover how we can use Pythagoras'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-angled 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. The 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. Once we've labeled c the other two sides will always be a and b and it doesn't matter which way around 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 correspond to each letter into the equation. So because A is 4 and B is 3 we'd write 4 squared plus 3 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 5 equals c. So the length of x must be 5. 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 in 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 to 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 examine 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 through 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.