Uses Of Pythagoras Theorem | Trigonometry | Maths | FuseSchool

You should know by now what Pythagoras theorem is and how to use it but if you'd like to refresh your memory watch this video. So we know that if we have a right angle triangle with the sides a b and c where side c is opposite the right or 90 degree angle then c squared equals a squared plus b squared. But what's it used for? One useful thing you can use Pythagoras theorem for is to find the distance between two points using their coordinates. If you don't know how to work with coordinate plane watch this video but if you know what it is let's try to find the distance between two arbitrary points. Assuming that we have two points a with coordinates five two and b with coordinates nine five what's the distance between them or in other words what is the length of the line segment a b. The problem is that we don't know how to count distance diagonally yet only using axis but Pythagoras theorem can fix that. First let's find horizontal and vertical distances between the two points. We need two additional lines for that let's name the intersection point c the angle a c b is the right angle or 90 degree angle so b c equals five minus two which equals three and a c equals nine minus five which is equal to four. Does it remind you of something? Yes we've got two sides for Pythagoras theorem so now we can use it to find the third one so the length of a b is the square root of 25 which equals five. Let's summarize how can we find the distance between two points well it's pretty easy first find the horizontal distance between the points then find the vertical distance between the points and finally use Pythagoras theorem to find the length of the hypotenuse which is the distance we are looking for. For those of you who like formulas here's what it is if we have two points a and b then we can always use the following formula to find the distance between these points. This looks scary doesn't it but let's gather our courage and look closer this is just another representation of Pythagoras theorem. So why do we do all these strange things because now we can find the distance between objects even without drawing them you may say but we like drawing graphs it's fun well not everyone likes pictures for example computers hate pictures because they don't even understand what they're looking at but they like numbers and they can count really fast. Computers know the position of the object because they know its coordinates and that makes our lives easier because we can explain to our computers what the distance is using this scary formula. So let's use it imagine that we are playing a very easy computer game there are two objects on the screen a boy and a zombie the boy is trying to run away from the zombie if at any point in time the distance between the boy and the zombie becomes less than 20 points it catches the boy and forces him to do maths exercises but if the boy runs away increasing the distance to more than 100 points from the monster he escapes and wins. Our computer only knows the coordinates of the boy and the zombie but we now know that this is the only data it needs to find the distance so our command to the computer will look like this if the value of this expression is less than 20 go and study maths and if the value of this expression is more than 100 then the player wins let's play help the computer find the result of the game if the zombie's coordinates are 19 28 and the boy's coordinates are 31 37. You aren't a computer so feel free to use any method you like and that's how Pythagoras helped us create computer games don't forget to thank him next time you play one if you like the video give it a thumbs up and don't forget to subscribe comment below if you have any questions why not check out our physical app as well until next time