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find-x-




Question Number 104877 by  M±th+et+s last updated on 24/Jul/20
  find x
$$ \\ $$$${find}\:{x} \\ $$
Answered by ajfour last updated on 24/Jul/20
Commented by  M±th+et+s last updated on 24/Jul/20
well done sir
$${well}\:{done}\:{sir} \\ $$
Commented by ajfour last updated on 24/Jul/20
(π/2)+α+((2π)/5)=π   ⇒  𝛂=(π/(10))  β=(1/2)((π/2)+α)=((3π)/(10))  sin 𝛗=((a/2)/a)    ⇒  𝛗=(π/6)  𝛗+𝛃 = 𝛑−2x  ⇒   x=(𝛑/2)−(𝛃/2)−(𝛗/2)              = 90°−27°−15°        ⇒   x = 48° .
$$\frac{\pi}{\mathrm{2}}+\alpha+\frac{\mathrm{2}\pi}{\mathrm{5}}=\pi\:\:\:\Rightarrow\:\:\boldsymbol{\alpha}=\frac{\pi}{\mathrm{10}} \\ $$$$\beta=\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\pi}{\mathrm{2}}+\alpha\right)=\frac{\mathrm{3}\pi}{\mathrm{10}} \\ $$$$\mathrm{sin}\:\boldsymbol{\phi}=\frac{{a}/\mathrm{2}}{{a}}\:\:\:\:\Rightarrow\:\:\boldsymbol{\phi}=\frac{\pi}{\mathrm{6}} \\ $$$$\boldsymbol{\phi}+\boldsymbol{\beta}\:=\:\boldsymbol{\pi}−\mathrm{2}\boldsymbol{{x}} \\ $$$$\Rightarrow\:\:\:\boldsymbol{{x}}=\frac{\boldsymbol{\pi}}{\mathrm{2}}−\frac{\boldsymbol{\beta}}{\mathrm{2}}−\frac{\boldsymbol{\phi}}{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:=\:\mathrm{90}°−\mathrm{27}°−\mathrm{15}° \\ $$$$\:\:\:\:\:\:\Rightarrow\:\:\:\boldsymbol{{x}}\:=\:\mathrm{48}°\:. \\ $$

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