mathematics.docx

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.