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Right Triangles in Real Life

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hello and welcome to the next topic and Unit 13 which is right triangles in real life we're going to talk about today is how this stuff we're learning about right triangles and Pythagoras and all that stuff is important and useful like for instance let's say you were at Talbert Middle School and you spent all day learning at the end of the six. The bell rings and you decided to walk home so let's say you walked East on brabham drive and let's say you went about 750 before you got to Hickory Lane and then you walked me for about eight hundred feet and by the time you got to the edge of that Greenbelt your friend's texts you and your friend says to you hey did you know that you forgot your math book it's I'm right here on the grass in front of the school and so you have to walk all the way back but this time you go across the Greenbelt across the grass across the blacktop to the library in a straight line how far did you have to walk back did you have to walk 700 + 800 know you went a shorter route but how much shorter what is that distance well basically is this not simply a right triangle yes because brabham and Hickory are perpendicular to each other like many streets are this scenario forms a right triangle and in any right triangle you can always use the Pythagorean theorem which says that leg squared plus leg squared equals hypotenuse squared 700 and 800 or the legs X is the hypotenuse cuz it's the Crooked one it's the longest one it's when it's not touching that right angle and now all we have to do is solve this problem so 700 x 100 is 44 and 190800 * 800 is 640000 and then you add those together you get 1 million 130 thousand and then to get X you got an unsquare that so that we know what x is and when you unsquare that the answer to our problem is about 1063 feet now you have to say about because that square root didn't come out perfectly nice and even and we had to round up a little bit but basically this is just a Pythagorean theorem problem in Disguise as a word problem and what I want you to understand today is that we can do this with all kinds of word problems because right triangles are that's right right triangles are everywhere in fact there in all kinds of sports right triangles are in origami and woodworking they even are in ancient artifacts and history and they or even in its current artifacts of current history of Nations that exist today and all kinds of symbols of national pride have right triangles built into them and even the that you fold some of these symbols of national pride and store them have to do with right triangles impact right triangles also happen when the sun casts a shadow right triangles also happen playing up in the sky has to communicate with an air traffic control tower and when satellites up in the sky communicate with the Earth they make right triangles in fact. first and the Sun and the Stars way way way outside of our solar system can make right triangles and that's how we calculate astronomical distances and it's also how we can calculate not so astronomical distance it's like how far a boat is off of the shore that's another right triangle scenario where else are right triangles well right triangles and roller coasters while we're not going to talk about ladders right triangles or even an ugly Hair Designs Korean shaped birdhouses right triangular even in the way some of you cut your sandwiches and of course right triangles are found in the design of the famous high pop that was a bad one where else are they interior design uses right triangles all the time and exterior design uses right triangles all the time and how to make those designs come to life construction and architect workers use right triangles all the time right triangles there everywhere so since we can't escape triangles we can't avoid then they're all around us let's learn how to use them to help us solve math problems like this suppose you're making a sale in the shape of a right triangle for a sailboat the length of the longest side is 65 you can read the rest of what we're trying to do here is figure out how do we solve this word problem but we're comes are too hard to do in your head whenever you have a word problem like this here's what you have to do sketch it out take all those words and turn it into a picture you know what to say looks like and you know what I say oh on a sailboat looks like so draw a little sailboat it doesn't have to be a work of art you just have to get it so that you know oh hey a sale is shaped like a right triangle and I know stuff about right. so I know how to solve this problem all I have to do is look at the numbers here figure out where to put them on my diagram and then I'll be good to go will says it's 63 feet high so you're going to label the height is 6 it says the sale is 65 ft on the longest side of that triangle we know that the longest side of a triangle is always the hypotenuse so that's where the 65 goes and is asking what is the length of the third side that's what don't know so we'll put an Axe and now we just need to turn this into an A Squared B squared c squared Pythagorean theorem equation so which two are the legs and which one is the hypotenuse well x + 63 EXO x squared + 63 squared equals the hypotenuse squared which is 65 squared I'm not even going to finish this problem cuz from here you can just do the math and use a calculator to figure out what x is going to come out to but the point is when you have a Pythagorean theorem word problem you've got to just sketch it out turn it into a picture turn it into a diagram turn it into a right triangle so here's some practice that I want you to try practice prime number one I don't like leaving school now you're leaving your house and instead of East you're going west and instead of North you're going south but can you turn that into a picture you can try it and see what you come up with oh no this one has so many words what are we going to do your shoot your locked out of your house the only open window is on the second floor okay I could fix her house and a window being up high and the window was 25 feet above the ground cuz I think I could now label that you need to borrow a ladder from one of your neighbors but there's a bush along at your house will need to place the ladder 10 ft where am I going to put 10 ft okay the base you'll need to put the ladder 10 feet from the house and what length of so X is the length of the ladder I think you could probably turn this into a picture that looks like a right triangle and then figure out how to solve the problem try that see what you come up with and we'll take a look monyana all right remember right triangles are everywhere and when you have to solve a problem sketch it out

Uploaded by Jeff Marbut.

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Right Triangles in Real Life

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