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PythagoraswasaguywholivedinGreecearound2600yearsago.Hefiguredouthowtousetrianglestocalculatestuff.Hiscalculationsweresogoodthatengineersstillusethosecalculations.
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HereareacoupleofexamplestoshowhowPythagorasisrelevanttoday.
EvencomputergamesusePythagoras.IncomputergamesXandYdistanceofashotisusedtocalculatethediagonaldistancetravelledbytheprojectile.Gaming
InarchitectureandhomerenovationalotofanglesandlengthsarecalculatedusingPythagoras.Architecture
Televisionscreensizeswereinitiallymeasureddiagonally.Todaywestillmeasurescreensthatway.Thesizeofyourflatscreen,smartphoneandtabletisdescribedasthelengthofthediagonalofthescreen.Pythagorasallowsdesignerstoaccuratelycalculatethediagonalsofdisplays.Engineeringanddesign
Cranesareusedinconstructionandshipping.Usingtrianglestobuildthecraneseffectivelydistributestheliftingforces.EngineersusePythagoras’scalculationstoknowhowfarandhighcranescanlift.Constructionandshipping
8.Skaterampexample
7.Samplecalculations
2.Theoryexplanation
3.Relevancetoustoday
6.Rightangletriangle
5.Squareroot
4.Squarednumber
RequiredKnowledge
1.Intro
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Communicatethecalculationbywritinganexponentoftwototherightandslightlyabovethenumber,forexample“3tothepoweroftwo”.
Thisiswhyweusetheword“squared”whenwemultiplyanumberbyitself.
Wecandrawthisasasquarewithsidesthatarethreeunitslong.Drawingoutthesquareshowsthattheareaofthesquareis9units.
Whenwemultiply3byitselftheansweris9.
Wesayanumberis“squared”whenwemultiplythenumberbyitself.
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Squarerootsareveryrarelywholenumbers,sopreparetouseyourroundingskills.
Theeasywaytogetthenumber,istoputthenumberintoyourcalculatorandpressthe“√”button.
Togetbacktotheoriginalnumber,weneedtofindwhichnumberwasmultipliedbyitselftogettothesquaredvalue.
Consequently,werefertoanumbermultipliedbyitselfasa“squared”number.
Theareaofasquareiscalculatedbymultiplyingthelengthbythewidth.Funnythingis,inasquare,thelengthandwidtharethesame!

hypotenuse
longside
rightangle
ClicktheplayicontowatchaquickdisplaydiagramofPythagoras’stheorem.
Witharightangledtriangleyoucanusethissumtocalculatethelengthsofthesidesofthetriangle.
Youdon’talwayshavetocalculatethelongside(thediagonal).Ifyouknowwhatthelengthofthediagonalis,andyouknowthelengthofoneside,youcancalculatethelengthoftheothershortsidebysubtraction.
Ifyoucalculatethesquarerootofanyofthesevalues,youwillfindthelengthofthatside.
isequaltothesumofthesquarevaluesonthetwoothersides.
Hesaidthat,inarighttriangle,thesquarevalueofthelongside
2600yearsagoPythagorasfiguredouthowtouseanytwosidesofarighttriangletocalculatethelengthofthethird.
shortside2
shortside2
longside2
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EQUALS
PLUS
IfyouneedtocrossaravineinasurvivalsituationPythagorasistheretohelp!Clicktheplayicontowatchtheexplanation.
unknownlengthIfIusePythagoras’stheoryIcancalculatethelengthofthelongsideofthetriangle,givingmetheminimumlengthneededfortherope.IfIthinklikearealnerd,itmeansthatIcanimaginearightangledtrianglebecauseIknowthelengthsoftwoofthesidesofthetriangle.Iguessit’sabout7metersaway.AndI’mguessingit’sabout3meterslowerthanwhereIamnow.Theoppositesideoftheravineislowerthanthisside.Aropeslidewillwork.3metres 7metres
Hereisthecalculationtodeterminethelengthofthediagonaloftheoverhang:
Ceilingheighttothetopoftheroofis1.2meters.
Thepatioextendsfor2.8metersfromthehouse..
Iambuildingapatioextensionatmyhouse.
2.8meters
1.2meters
d
=3.05m
d
=9.28m
d
=1.2m2+2.8m2
d
=1.2m2+2.8m2
d2
Iwanttobuildaskateboardslide.IthinkPythagoraswillhelpmecalculatethelengthofthepipethatIneedtocut.