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Indirect Measurement

Added Mar 04, 2019 •

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let's talk about something called indirect measurement we're talking about geometry congruence and similarity an hour and talk about how to use that has problems before we do that though show you a picture of the summit the peak of a mountain called Burke king or Burke Tong I'm not sure how you pronounce that this is a tall mountain in Nepal and it's actually named after this guy Bill Burke who actually lives only about 10 minutes away from Talbert Middle School and he is the oldest person to have ever climbed Mount Everest he climbed Mount Everest at the age of 73 in 2014 and so the people of Nepal named one of the Peaks after him which is kind of a cool thing that a mountain named after you now you can read about more about that at this link right here if you want to what I want you to know about the summit of this mountain is that it reaches a height of 6942 M which is 22775 feet I want you to know that there's something interesting about this mountain peak nobody has ever climbed it nobody has ever climbed it so the question is how do we know that that's how tall it is if nobody is actually ever been up there in fact how do we know how tall any mountain is you can't measure a mountain with like a measuring tape or a ruler right how do we know the heights of mountains well the answer is what we call indirect measurement when you can't measure something directly with a ruler or yardstick or a measuring tape you have to find other methods and now gives us indirect measurement indirect measurement is a technique that uses properties of similar polygons similar we've seen that word to find distances are lengths that are difficult to measure directly in other words what we can do is we can find the heights of mountains that are really tall or we can find the distance across a river without having to swim across it or we can even find the diameter of the Moon which we definitely can't measure with a ruler or yardstick using indirect measurement instead of direct measurement so how does this work the way it works is by using similar triangles or some other kind of similar shape but it's usually triangles so here's how it would look with the mountain if you want to know how tall the mountain is we could make a triangle to represent the mountain now we can measure all the parts of that triangle but we could make a similar triangle that is a size that immeasurable by us and if we know the size of the smaller triangle then we can use the properties of similar triangles to help us understand the measurements of the larger triangle indirect measurement so here's an example of what might actually look like a 5-foot person is standing near a tree and the person cast The Shadow that's 12 12 ft long the tree also casts a shadow that is 42 ft long what's the height of the tree just one we got a sketch this thing out so that we can visualize it so here's a quick sketch there's a tree we don't know how tall it is and its shadow is 42 ft long there's a person we know their height their size he talked and we can measure their Shadow is 12 feet long so we can use this to help us discover the height of the tree and we don't have to actually directly measure the height of the tree we can use proportions because we know similar triangles have proportional relationships so I'm going to say that X over 5 equals 42/12 and then step 3 as well we're gotta do some cross multiplication and solve this thing so we're going to have 12 times x equals five times 42 and then we're going to multiply 5 * 42 in / 12 and eventually use our calculator and get that x equals 17.5 so what is the height of the tree the tree is 17 and a half he talked and we didn't need to measure the tree we just measured a couple shadows and the height of a person this is what we call indirect measurement and when you use Shadows to do it it's what we call a special kind of indirect measurement Shadow recognize which is kind of a cool phrase it kind of like yeah anyways the first person that we know of in human history who performed at Shadow Reckoning was an old that Greek guy named thales thales lived about 2,600 years ago so long long long time ago Bailey's really impressed people by finding the height of one of the Great Pyramids of Egypt but of course he didn't measure it Direct he just used Shadow Reckoning to find the height of the pyramid and of course everybody was super impressed and I thought wow thales this is amazing you're so intelligent look at you your eyes have no pupils are red that's actually that's kind of creepy but we like you anyways because you're so smart anyways Shadow Reckoning so if you ever start like a band like No Quarter band and you're looking for a good name if you could call anyways how about you try to do a little Shadow Reckoning you try to do a little bit of indirect measurements here using similar triangles so read this problem maybe pause the video and then see if you can do step one dried-out do step to make some proportions and then do step 3 solve the proportion to come to an answer in fact okay okay I'll do the drawing for hopefully you can see how that drawing relates to that word problem and what the heck I'll just go ahead and make a proportion for you X over six equals 9/4 make sure you can see the connection between that drawing and those proportions if not write down a question or put a starter or something so that we can talk about this tomorrow then of course we're going to cross multiply 4 times x equals 6 X 9 and if you just go ahead and give you the answer of 13 and 1/2 feet all right if you can do this problem you're doing indirect measurement and is really just an extension of what we learned about similar triangles or similar figures I think this is pretty cool and I think it makes a lot of sense and hopefully taking good notes and we can do some more indirect measurement in class tomorrow alright see you later

Uploaded by Jeff Marbut.

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Indirect Measurement

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