mathematics.docx
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mathematics
GAC004AssessmentEvent2:
Project-Trigonometry
Aresearchabouttriangle
StudentName:
Kate
StudentID:
ZXET31872
Teacher:
Shirley
DueDate:
15/November/2014
WordCount:
461
TableofContents
Introduction1
Obtusetriangle2
Calculationandcompare5
AcuteTriangle6
Calculationandcompare9
Conclusion9
Introduction
Today,wetrytomarkpointsoutsideonaflatgrassyarea,madeanobtuseandacutetrianglewithribbons.Thenusethemeasurevaluetoprovesine,cosineandarearule.
Obtusetriangle
A
c
b
B
C
a
Lengthofais177cm
AngleofCis40°Thelengthofcis128cm
Setupperpendicularheightofthetriangle.
Thelengthofbis73cmThelengthofhis47cm
Calculationandcompare
A
cb
B
C
a
∵AngleC=38°
Lengthofb=73cm
Lengthofa=177cm
∴Lengthofc=a²+b²-cosC*2ab=128.4≈128cm
Andthemeasuringthelengthofcis128cm.
Thereisonlyaslightdifferencebetweenthecalculateresultandmeasuringresult.SowecanknowtheSineruleisclearlycorrect.
∵Thelengthofh=47cm
Thelengthofa=177cm
∴S=1/2(a*h)=1/2*1.77*0.47=0.41595
∵Thelengthofa=1.77m
Thelengthofb=0.73m
AngleofC=38°
∴S=1/2(a*b*sinC)=1/2*1.77*0.73*sin40°=0.4153≈0.41595
Thereisonlyaslightdifferencebetweenthecalculateresultandmeasuringresult.Sowecanknowthearearuleisclearlycorrect.
AcuteTriangle
A
cb
BC
a
a
Thelengthofais125cm
AngleofAis58°TheangleofBis60°
Thelengthofbis126cm
TheangleofCis62°Thelengthofcis129cm
Calculationandcompare
∵Lengthofa=1.25m
Lengthofb=1.26m
Lengthofc=1.29m
∴cosA=0.5210AngleofA=58.6°≈58°
cosB=0.5045AngleofB=59.7°≈60°
cosC=0.4726AngleofC=61.8°≈62°
a/sinA=1.4637
b/sinB=1.4583∴a/sinA=b/sinBc/=sinC
c/sinC=1.4626
ThencomparewiththemeasuringresultsthereisonlyaslightdifferencesotheruleofCosineiscorrect.
∵Thelengthofais1.25m,
Thelengthofbis1.26m,
TheangleofAis58°
Throughthesinrule,wecangettheresultofsinB=sinA*b/a=0.864AngleB=59.7°≈60°
Wecanseethatthereisonlyalittledifferencebetweenthecalculatevalueandthetruevalue,sowecanknowthesinruleiscorrect.
Conclusion
Accordingthevalueswemeasuredandthencomparewiththearithmeticvalues,a/sineA≈b/sineB≈c/sinC,S=1/2*ah=1/2*sinA*b*c,cosA=(b²+c²-a²)/2bc,becausethereisonlyaslightdifferencebetweenthem,sowecandrawaconclusionthatthesinerule,cosineruleandarearulearecorrect.