lprove that cosine rule theorem
for hav board exam
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Laws of Cosine or Cosine Rules
As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –
a2=b2+c2−2bccosx
b2=a2+c2−2accosy
c2=a2+b2−2abcosz
To find the angles x, y & z, these formulae can be re-written as :
cosx=b2+c2−a22bc
cosy=a2+c2−b22ac
cosz=a2+b2–c22ab
As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –
a2=b2+c2−2bccosx
b2=a2+c2−2accosy
c2=a2+b2−2abcosz
To find the angles x, y & z, these formulae can be re-written as :
cosx=b2+c2−a22bc
cosy=a2+c2−b22ac
cosz=a2+b2–c22ab
ankit4922:
i know the formula i want full proof
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Laws of Cosine or Cosine Rules
As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –
a2=b2+c2−2bccosx
b2=a2+c2−2accosy
c2=a2+b2−2abcosz
To find the angles x, y & z, these formulae can be re-written as :
cosx=b2+c2−a22bc
cosy=a2+c2−b22ac
cosz=a2+b2–c22ab
____________________________
Example -Find the length x in the following figure.
Solution: By applying the Cosine rule, we get:
x2=222+282–2.22.28cos97
x2=1418.143
x2=1418.143<
As per the diagram, Cosine rules to find the length of the sides a, b & c of the triangle are –
a2=b2+c2−2bccosx
b2=a2+c2−2accosy
c2=a2+b2−2abcosz
To find the angles x, y & z, these formulae can be re-written as :
cosx=b2+c2−a22bc
cosy=a2+c2−b22ac
cosz=a2+b2–c22ab
____________________________
Example -Find the length x in the following figure.
Solution: By applying the Cosine rule, we get:
x2=222+282–2.22.28cos97
x2=1418.143
x2=1418.143<
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