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Chapter5:ThreeFigureBearings
Core(2A&2B) Extension(2A)
• Interpretandusethree-figurebearingsmeasuredclockwisefromthenorth.
• Usescaledrawingsandtrigonometricalratiostosolveproblemsinvolvingbearings.
SECSyllabus(2015):Mathemtics
Section5.1WhatareBearings?
• Therearemanywaysofgivingbearingsordirections.ThemostcommonmethodistheoneinwhichNORTHisreckonedtobeZEROandanglesaremeasuredfromthenorthinaCLOCKWISEdirection.
• Usually3figuresaregiven.o 055°iswrittenfor55°.o 009°iswrittenfor9°.
• Inbearingswhenyoudrawanglesyoudonotneedtodrawaccurateangleswithyourprotractor(ifnototherwisestated).
Forexample,inthisdiagramthebearingofBfromAis060°.
Abearingcanhaveanyvaluefrom0°to360°.Itisusualtogiveallbearingsasthreefigures.Thisisknownasathree-figurebearing.So,intheaboveexample,thebearingistobewrittenas060°,usingthreefigures.Herearethreemoreexamples.
A
B
60°
N
N
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Thereareeightbearings,whichyoushouldknow.Theyareshowninthediagram.
Disonabearingof048°fromC.
Fisonabearingof110°fromE.
Hisonabearingof330°fromG.
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Example1:ThebearingofAfromBis080.WhatisthebearingofBfromA?
Example2:Drawsketchestoillustratethefollowingsituations.
a) Cisonabearingof170°fromH
b) Bisonabearingof310°fromW
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Example3:AisduenorthfromC.BisdueeastfromA.Bisonabearingof045°fromC.SketchthelayoutofthethreepointsA,BandC.
Example4:Drawdiagramstosolvethefollowingproblems.
a) Thethree-figurebearingofAfromBis070°.Workoutthethree-figurebearingsofBfromA.
b) Thethree-figurebearingofPfromQis145°.Workoutthethree-figurebearingsofQfromP.
c) Thethree-figurebearingofXfromYis324°.Workoutthethree-figurebearingsofYfromX.
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Section5.2BearingsandTrigonometry
Example1:TwofishingboatsstartsailingfromthesameplaceP.Oneofthemsails14kmonabearingof060°toarriveatpointA.Theotherboatsailsfor12kmonabearingof150°toarriveatpointB.
a) Drawasketchusingthisinformationb) Showthat∠APB=90°c) CalculatethedistanceAB.
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Example2:TwohikersdepartfrompointP.Johnwalksfor8kmdueNorthtopointAwhilePatrickcovers11kmdueEasttopointB.Find:
a) thedirectdistanceAB
b) thebearingofAfromB
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Example4:FromapointP,amanwalks9kmnorthtoQ,then5kmeasttoR.WhatisthebearingofRfromP?
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Section5.3:UsingtheSineFormulaandtheCosineFormulaforbearings
a. Bis10cmawayfromAonabearingof030°.Cis15cmawayfroAonabearingof055°.FindthedistancebetweenBandC.
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b. A,B,CandDarefourtowns.Bis9kmduesouthofA.Cis12kmdueeastofB.Dis15kmawayfromConabearingof020°.Find:I. thedistancebetweentownAandtownCII. thebearingofAfromCIII. thedistancebetweentownAandtownD.
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c. A,BandCarethreepointsonahorizontalplane.Bis12mawayfromAonabearingof020°.Cis15mawayfromAonabearingof050°.AVisaverticalpoleandtheangleofelevationatthetopofthepolefromBis35°.FindI. theheightofpoleAVII. thelengthofBCIII. theareaofbaseABCIV. thebearingofCfromB.
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Section5.4:Bearingandscaledrawings
Step1:Makearoughdrawingoftheobject
Step2:Markallfullsizemeasurementsonthediagram.
Step3:Drawanothersketchandputthescaledmeasurementsonthisone.
Step4:Drawtheaccuratescaledrawing.
Example1:Fromoneend,A,ofaroadthebearingofabuilding,L,is015°.Theotherendoftheroad,B,is300mdueeastofA.FromBthebearingofthebuildingis320°.Usingascaleof1cmto50m,makeascalediagramtofindthedistanceofthebuildingfromA.
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Example3:ThediagramshowsthepositionsofthreeBritishcities:London,NottinghamandBirmingham.
a) Whatisthebearingof:i. NottinghamfromBirminghamii. LondonfromBirminghamiii. BirminghamfromNottingham
Nottingham
London
Birmingham
43°
48°
45 miles
100 miles
N
N
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b) Use1cmtorepresent10miles,drawascalediagramtoshowthepositionsof thethreecities.HencefindthedistancefromLondontoNottingham.
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