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Question-133069




Question Number 133069 by Dwaipayan Shikari last updated on 18/Feb/21
Commented by Dwaipayan Shikari last updated on 18/Feb/21
One can stretch and reform sides AB  and AC , by   considering length  BC as constant. the angle   φ can change. Find the relationship of changes between Side   AB , AC and angle φ  (Assuming that the triangle will not break ,and lengths are  interelated)
OnecanstretchandreformsidesABandAC,byconsideringlengthBCasconstant.theangleϕcanchange.FindtherelationshipofchangesbetweenSideAB,ACandangleϕ(Assumingthatthetrianglewillnotbreak,andlengthsareinterelated)
Commented by mr W last updated on 18/Feb/21
BC=a=constant  AC=b=variable  AB=c=variable  ∠A=φ=variable  b^2 +c^2 −2bc cos φ=a^2   or  (b−c)^2 +2bc(1−cos φ)=a^2
BC=a=constantAC=b=variableAB=c=variableA=ϕ=variableb2+c22bccosϕ=a2or(bc)2+2bc(1cosϕ)=a2
Commented by Dwaipayan Shikari last updated on 18/Feb/21
b^2 +c^2 −2bccosφ=a^2   ⇒2bb^. +2cc^. −2b^. ccosφ−2cb^. cosφ+2bcsinφφ^. =0  ⇒bb^. +cc^. +bcsinφφ^. =cosφ(bc^. +cb^. )  Can we do further like this?
b2+c22bccosϕ=a22bb.+2cc.2bccos.ϕ2cbcos.ϕ+2bcsinϕϕ.=0bb.+cc.+bcsinϕϕ.=cosϕ(bc.+cb.)Canwedofurtherlikethis?
Commented by mr W last updated on 18/Feb/21
yes
yes

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