PRESENTER:Pythagoras' theorem sounds a bit complicated, so what is it in a nutshell?
PRESENTER:Well, it's actually pretty simple really.
PRESENTER:When we have a right-angled triangle and we know the lengths of two of the sides, we can calculate the length of the third, using an easy equation.
PRESENTER:With a right-angled triangle
PRESENTER:the square of the hypotenuse, the longest side of the triangle,
PRESENTER:is equal to the sum of the square of the other two sides.
PRESENTER:So,
PRESENTER:A squared plus B squared equals C squared.
PRESENTER:Now let's give them some figures.
PRESENTER:If we had a triangle with the lengths three, four and five cm, would it have a right-angle?
PRESENTER:Well using the equation, we have three squared plus four squared equals five squared. So nine plus 16 equals 25. So yes, we have a right-angled triangle.
PRESENTER:Easy enough, right?
PRESENTER:Well, meet Jim.
PRESENTER:Say hello, Jim.
JIM:Hello.
PRESENTER:That's Jim. He's a window cleaner.
JIM:I'm a window cleaner.
PRESENTER:And he needs to reach those windows, which are quite high up.
JIM:I'm afraid of heights.
PRESENTER:Not now, Jim.
PRESENTER:'Now we know that the length of the ladder is four metres, and the base of the ladder will be placed one metre away from the wall.
PRESENTER:'So what height will the ladder reach? Well if we are calculating the length of any side apart from the hypotenuse, which is always opposite the right-angle, we amend the equation.
PRESENTER:'So C squared minus A squared equals B squared. Which means four squared minus one squared will be equal to B squared. And 16 - 1 =15.
PRESENTER:'So the height is equal to the square root of 15, which is 3.87m, to two decimal places.'
PRESENTER:So now Jim can get started on these windows.
PRESENTER:Meet Dave.
PRESENTER:Dave is buying a new TV. Say hello, Dave.
DAVE:Hello.
PRESENTER:That's Dave.
DAVE:I'm getting a new TV because I made a PPI claim–
PRESENTER:Not now, Dave!
PRESENTER:'Now the space we have available is 32 inches in height and 45 inches in width, and the length of the diagonal will indicate what size TV screen can fit in this space.
PRESENTER:'So 32 squared plus 45 squared equals C squared. Which means C is equal to the square root of 1024 plus 2025, which equals 55.218, to three decimal places.
PRESENTER:'So the maximum size TV that Dave can fit here will be a 55 inch TV.'
PRESENTER:And that's all there is to it. Comes in quite handy, too.
Video summary
The short clip demonstrates the theory of Pythagoras by showing how to calculate the Hypotenuse of a right-angled triangle and by using numbers it proves that the triangle is right angled.
The clip progresses to show the practical applications of Pythagoras by calculating the height at which a ladder against a wall reaches, and solving the problem of what size TV will fit in a particular space.
This is from the series: Real Life Maths.
Teacher Notes
Teachers can use the video clip to demonstrate how to apply Pythagoras and help pupils solve potential exam questions.
The learners could be arranged in a carousel arrangement; where they tackle exam questions with different skills such as calculating the shorter side, and proving that a triangle is right angled.
Using the video clip as support, Pythagoras lends to a variety of practical solutions.
So we could place learners in groups of 3 and take pictures around the school; where they would have to solve problems using Pythagoras.
The learners could feedback in a presentation format to the class.
This clip will be relevant for teaching Maths at KS3/GCSE in England Wales and Northern Ireland. Also at National 4, 5 and Higher in Scotland.
This topic appears in OCR, Edexcel, AQA, WJEC in England and Wales, CCEA GCSE in Northern Ireland and SQA in Scotland.
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