mathematics.docx

1、mathematicsGAC004 Assessment Event2: Project-TrigonometryA research about triangleStudent Name: KateStudent ID: ZXET31872Teacher: ShirleyDue Date: 15/November/ 2014Word Count: 461Table of ContentsIntroduction 1Obtuse triangle 2Calculation and compare 5Acute Triangle 6Calculation and compare 9Conclus

2、ion 9IntroductionToday, we try to mark points outside on a flat grassy area, made anobtuse and acute triangle with ribbons. Then use the measure value to prove sine, cosine and area rule.Obtuse triangle A c b B CaLength of a is 177 cmAngle of C is 40 The length of c is 128 cmSet up perpendicular hei

3、ght of the triangle.The length of b is 73 cmThe length of h is 47cmCalculation and compare A c b B Ca Angle C=38Length of b=73cmLength of a=177cmLength of c=a+b-cos C*2ab=128.4128cmAnd the measuring the length of c is 128 cm.There is only a slight difference between the calculate result and measurin

4、g result.So we can know the Sine rule is clearly correct.The length of h=47 cmThe length of a=177 cmS=1/2(a*h)=1/2*1.77*0.47=0.41595The length of a=1.77mThe length of b=0.73mAngle of C=38S=1/2(a*b*sinC)=1/2*1.77*0.73*sin40=0.41530.41595There is only a slight difference between the calculate result a

5、nd measuring result.So we can know the area rule is clearly correct.Acute TriangleA c b B CaaThe length of a is 125 cmAngle of A is 58 The angle of B is 60The length of b is 126 cm The angle of C is 62The length of c is 129cmCalculation and compareLength of a=1.25mLength of b=1.26mLength of c=1.29mc

6、os A=0.5210Angle of A=58.658cos B=0.5045Angle of B=59.760cos C=0.4726Angle of C=61.862a/sinA=1.4637b/sinB=1.4583 a/ sin A=b/ sin Bc/= sin Cc/sinC=1.4626Then compare with the measuring results there is only a slight difference so the rule of Cosine is correct.The length of a is 1.25m,The length of b

7、is 1.26m,The angle of A is 58Through the sin rule, we can get the result of sin B=sin A*b/a=0.864 Angle B=59.760We can see that there is only a little difference between the calculate value and the true value, so we can know the sin rule is correct.ConclusionAccording the values we measured and then compare with the arithmetic values, a/sine Ab/sine Bc/sin C, S=1/2*ah=1/2*sin A*b*c, cos A=(b+c-a)/2bc, because there is only a slight difference between them, so we can draw a conclusion that the sine rule, cosine rule and area rule are correct.