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Pre-Algebra 6.9 Indirect Measurements

Added Apr 25, 2021 •

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Setting up Proportions with Corresponding Parts to Solve and Find a missing measurement

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measurement all of this stuff has to do with proportions you can always do stuff with proportions all right we know what's similar figures similar figures corresponding figures solving problems involving indirect measurement using Shadow Reckoning there's other for this this is a this is a new term for me shadow Reckoning I have never heard of that but I guess it's a new thing new way of describing the same thing that I've did solve problems using surveying methods surveying methods Justin's observation and looking for patterns survey when you survey something you just look at stuff and you take down characteristics all right on a sunny day you can see your Shadow the length of the Shadow around you are proportional to the height of objects casting the shadow so look at this right here this is something to use in real life and noticed right here they also used with right triangles I do this a right triangle has one of the most important things in engineering Pythagorean theorem basic stuff calculus is based on the Pythagorean theorem so everything is triangle and rectangle base and you'll star see that is patterns and the high you get in math towards your engineering even in business you use business you'll still use triangle so how tall is this person sitting on the judges at 10 it's obviously you know they climb up missed it right there. I got you a no-fault double Falls so it's harder to measure height it's easier to measure Mike down here cuz we got to climb up so look at this right here if you're standing the Sun hits you at a certain angle so the sun summer up here and the creates a shadow and it creates something that's proportional so if you know how tall you are we chose meters to meters is a nice measurement is based pain if you are 1.8 meters tall and your Shadow is point in or why and then the register is 1.2 M wide you can actually figure out how tall something is so if you're able to measure the length of a shadow of you and something else Kakashi figure out how tall something is like a tree so what kind of triangles are formed I already gave it to you a right triangle could tell right there 90° that's why you got to stand straight up so you form a right angle the bass the floor the ground make a conjecture how could you use your Shadow to determine the height of another object so right here so it's proportional right triangles are similar not all right transitional but the two triangles that are formed are similar they're the same and you can even find this length right here the hypotenuse a squared plus b squared equals c squared that's the Pythagorean theorem so indirect measurements allow you to use the properties of similar triangles to find measurements that are difficult to measure directly as the whole thing is awesome and is a tape measure what's the time I can't reach that person without a ladder myself but this I can measure easily The Shadow so the least some of them all right one type of indirect measurement is called Shadow Reckoning two objects and their Shadows form two sides of similar triangles so someone is already did it thank you let's tell someone didn't want me to do it so how to use set up a proportion and there's so many different ways so let's let me pull this triangle out just so we can visually see it we don't know how tall it that's why it's h this is one point to this little triangle is similar and one 8 vs 0.8 I remember setting it up as a cross product when things are similar when objects are similar the proportion are the same h / 1.2 if I go here to here on the other train I need to go the same direction 1.8 2.8 let's say I don't do that let's say a H the 1.8 so I do the same triangle to the same triangle I go from one side of the triangle to the other side of the triangle / 1.8 if I do that it needs to follow same direction 1.2 2.8 but looks totally different or I could start at the bottom first you know but I can't Z zig zag is the only thing but whiskey about this look at this my cross product that's still H * 28 equals 1.2 * 1.8 look at this cross-body right here age * 2.8 the only difference is these two are switched around as long as you follow an organized Direction and organized flow it doesn't matter how you set it up as it's organized but if I go zig zag here's a thing like this I go along side of one triangle to the short side that means in the oven Lawnside the short side but if I long side of one triangle to the long side of the other triangle versus notice I have to go in the same direction I started in this triangle have to go triangle want to try and go to short side Portside triangle 1 to Triangle to I can't zig zag I can't go long side to the other triangle short side I can't but you can buy just can't zig zag that you can look at this no no no you can't long side to the short side actually not make the same thing lawnsite to the short side let's look at that age 2.8 long side to the other triangle short side long side to the other channel no it does not work no just got to differ this one doesn't work so there's no order the order doesn't make sense right there Longshot if I compare the long side of one triangle to the short side of the other the long side of it doesn't flowing that so you got to make sure that you have the correct flow this right here going a let me just divided by 2.8 to make it equal so age I got 1.2 * 1 Point 8 / 8.8 I'm going to get rid of one of the decimals to make that at 12 that means I could never bye-bye for I get to if I divided by 4 I get three move over another decimal by get rid of that and then is over I get a 20 that becomes 18 and divide that by 2 I get a 10 / 2 I get a 9 27 10 2.7 knowing how to manipulate decimals and fractions this is a skill that so many drive me to work on in practice how do you do this quicker it's just practice so that's how tall the umpire's chair is so let's go look at this right here the lead statue of the Korean War Memorial in Washington DC I went I drove by it I didn't stop by it cast a 4.3 in Shadow at the sea time a nearby tourist cast a 32in shadow and you get to watch on the STAAR test on the STAAR test you guys need to watch out right now it's nice inches don't forget to pay attention to your units if they're different units you've got to watch out member converted it satirist is 64 in tall how tall is the lead statue and you can find it in inches converted to feet if you want so right now let's go look at this picture so it's up to you to decide how you want to match it up so don't want I'm going to go H to 4.35 the height of the Statue to 43.5 is 2 the height of the person to the shadow length I chose this because I can simplify this fraction watch this if I want to height to height H 264 versus so Shadow to real life person that person holding a basket as a side pouch ball height hi versus Shadow to Shadow notice how that flows where is this right here was height to the shadow height to the shadow so cross product age * 32 vs 43.5 * 64 cross products and cross product but look at this version right here I can simplify this 64/2 is the same thing 2 / 1 this version right here made it so much easier H * 1 is just H and then 43.5 * 2 that's all I have to do this cross product 32 h equals 64 * 43.5 and then I divided by 32 you can still see right here with 54 / 32 a2h equals 2 * 43.5 it's just I did a little bit more work and I still ended up the same thing I double 43 what's double 43 80s 86 + 1 87 in pay attention to the units a wrong answer could be to be if it's multiple choice like the ren star is 87 in 87 ft 87 M 8.7 ft stuff like that 87 how did they set up Dave flipped it over so they went person to the height person to the height versus person Shadow 2 statue Shadow and look at still created and look what they did they actually multiply that all the way through and then divided by 30 that's your choice they multiplied it on through I said forget that I want to multiply that number understanding fractions when you can simplify your fraction dealing with smaller numbers creates less of a chance to make errors in math when you play with bigger numbers I don't like what they did but they still did it right the tourist height is two times the length of his or her show is that a his or her I don't know is a statue should be two times its shadow to so which is try and do number one of your own and we'll do that call is the tower so you don't need to draw a tower but you can draw yourself something nice and simple ears hurt our ears okay I messed up I fell that's my belt that's a bell tower that's a horrible Belltower who cares stop laughing here's my shadow so I know my shadow that's that's the Shadow the shadow is 27 point text we're looking for the height of the Shadow here's my 6-foot person who is horrible at basketball a waste of height we know that this person is 6 ft call and we know their Shadow is 1.2 so notice it's a quick. All right all mushroom fine but you do even have to draw the belly you a line that's good enough what you guys think I see a lot of guys when I say sketch something out you guys give me some super detailed picture alright you can do that but you don't have time to do that on a test just a quick sketch that's a good sketch I don't care if that's I don't know the gender of my person that sticks person is supposed to represent a person keep it simple and you decide how you want to set up I'm going to show you this time this time I'm going to go H over I'm going to go h / 27.6 and this right here is just number sense me knowing how to look at things and relate them h / 27.6 I'm going with the same I burst is 6 / 1.2 here's why I'm going to do that I'm going to get rid of my decimal here's my desk so understanding how to get rid of decimals some of your teachers taught you that * 10 forever however many you got I'm just lazy here's one decimal place here's my decimal right here I'll put a zero as a placeholder to have the same amount of decimal places if I get rid of a decimal that makes this 12 that means I move the decimal right here move it over one time to the right that means I got to move this over one time to the right look at this h / 27 points equals that 60/12 here I'm going to do that over here 60 / 12 what's 60 / 12 V so that's 5/1 what again this is practice this is years of practice I have that on you guys are way better than yet basic arithmetic so look at this cross product 8 * 1 is just eh all I have to do is multiply 5 * 27.6 I always like to try and simplify my work my fraction components before I even try to multiply no matter what your Force the X all I have the X compared to whatever the message you got so 27.6 * 5 - 103 5 at Miro that's what a thousand 83 and then one decimal place 138th it's not hard as you guys think learning this is the thing it took me years to understand all these different things I could do to manipulate number you guys are learning it way earlier than I did it was until the end of high school that I have to do things that much quicker some of you guys even if you get the right answer mentally are considered a c student understand not bad you still got it right understanding how to manipulate numbers to make it easier that's what may people's stomachs better than me I didn't fail I dropped out of computer science because I couldn't think like that you can do that same thing the same thing is the cross product H * 1.2 let's finish that out couple people did it so let's say I didn't do the cross let's say I didn't simplified let's say it I did not simplify you can still do it that way 1.2 * 8 equals 6 * 27.6 the habit of this person right here would love to multiply this out and then / 1.2 but I like to get my variable by itself first so I create this ginormous looking looking weird traction with decimals and then here you could divide you do the same thing Deca / 1.2 + 6 same thing so you this 1227 point 6 divided by 12 and then X then x 6 same thing no difference you still get the same answer you know what you don't realize this right here that's 5 5 * 27.6 which is 130 same answer multiple ways of seeing things we're trying to get you guys somebody said the cross product is not needed no it's just a Prosperity is Just a way to organize your thoughts so it's a visual aid for a some of you guys are able to see the equation right away you have a way of seeing things but know that that's your one level up that's great but be able to does it mean you have be able to know that there are other ways of setting it up its symbols math screws up a lot too because how we write things out looking to in the figure triangle spu is similar to Triangle b q u find the disk across the pond this is the most common thing so look at this right here they created two triangles and notice they're flipped they're not facing the same way that's why I always base it on this I'm going to read I'm going to go s t you cuz with s t u s t u here's my ride Melissa you I'm going to redraw this triangle before I even do anything else letters points there now I'm going to go back the next train is V2 u s t u v q u i r e draw the triangle before I put on the second set of coordinates now I go back and put in my my measurements so I can match them up SE is 20 UT is 10 and let's look at this you to q q u e r s q u now to put the round of 16 nqv is ex now notice how everything space the same way all you got to do is set up a proportion I'm going to do this I'm going to a 20 / 10:20 / 10 cuz that becomes just equals if I went from bottom to the side bottom to the side x 216 let's take a cross product this suffice to chew over one I take lacrosse x equal x * 1 equals 2 * 16 I make a cross make sure it's only the equal on the inside two times 16x equals 32 Germaine surveying just pretty much uses things that mean they're not Shadows serving just needs looking at this time looking at observing this I'm looking at it and I turn things around made it some of you guys are good enough that you don't need to read rot I like to match things up that's me and again cross products not needed if you guys are good at 32 they did they decide to just a multiply straight up 20 * 1610 * X 10 X 63 simplify first just cuz I like to deal with smaller numbers I freaked out with big numbers this is like what I freak out when I go to no want to go to Baskin-Robbins too many choices right here with let's just quickly go over this do we have time yeah we have time for any time even in the figure you guys do this first try it out and figure triangle QRS is similar that's a symbol for similar triangle QRS is similar to Triangle Urt by the distance from the cabin to the mess hall who cares that's just there but they're already labeled it for you set it up solvit I will start with my first rental QRS q r s and things should go in the same or it's up to you if you want to put the measurements in before you draw your other triangle if you want to do that it doesn't affect it so this is X and this is a hundred 38th and then I'm going to drop my other triangle the same way notice I'm not labeling anything yet if the angle QRS QRS knows the whole thing I want this way for a hot SEC QRS notice the order the order of labeling the coordinate the letters of points for the next time you should follow the same thing Q are asked should match up with u r t and then now I'm going to look up see you notice how its flipped around so I look at the point r2t is 46 but instead it's ER now it's the same thing just turned around r2t instead of going left to right it goes right to left but it's the same side crrt is 46 and then are you is you are that's 60 so set it up however you want I will go and I know I'm your ex / 60 equals silent from this triangle to this triangle so that means I got to go from this side to this side 138 / 46 * 62 multiplying or dividing so multiply both sides by 60/1 cuz that becomes an x * 60 / 1 now before I simplify X let me let's / 2 / 2 that makes this 23 / 2 I get 30 can I go 138 and 23 say anything to buy that I don't know so I have a brain fart right now is 138 divisible by 46 I don't know I didn't see that I just decide to simplify that first in / 2 let's divide 138 and 28 * 6/6 23 * 6 + 20 time 6 18 carrier 112 138 all right / 23 if I / 23 that makes this 6 so what do I have left on the denominator 1 * 1 6 * 3180 180 / 1X equals 180 watch out again so Cairo 180 but the word problem is in measurements yards so think about multiple choice test even on the numbers right you got to think sometimes you guys go for the straight on a multiple choice test you got a lie add a different options you got a b c d and these are the nice multiple-choice problems does not nice ones to give you a v option so pay attention to your you guys got our different numbers are 21831 80s and a couple different ones with 18 on it or decimals different units pay attention to the units that are in the problem it was yard so make sure your guards mess up and saw and sometimes they'll do you dirty they sometimes do to your real dirty what if what if they don't have a yards in there what if yards not in there you need to find some because it freaked out I got one a they don't have a hundred 80 yards on their what's wrong before you freak out and cross out your work always check is there if this wasn't there I made some much if this is not there before you freak out a cross on throw away all your work check to see if one of the choices is equal to 100 yards it's just written differently in miles what if it was in inches they converted it and mess with you they would do something dirty like that to you so watch out

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Pre-Algebra 6.9 Indirect Measurements

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