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Question Number 182375 by Acem last updated on 08/Dec/22

Commented by Acem last updated on 08/Dec/22

$$Ijustsolvedit,2secago,$$$$\varphi \in ]20,27[$$$$BtwextendofNAintersectswithextendofPC$$$$atpoint\in thiscircle$$$$Hopeyousuccesstofind\varphi !$$

Answered by mr W last updated on 08/Dec/22

Commented by Acem last updated on 08/Dec/22

$$Nowyouransweriscorrect!verygoodandthanks$$

Commented by mr W last updated on 08/Dec/22

$$\cos \alpha =\frac{x^2+6^2-4^2}{2\times 6x}=\frac{x^2+20}{12x}$$$$\cos \beta =\frac{x}{2\times 6}=\frac{x}{12}=\sin \alpha$$$${\left(\frac{x^2+20}{12x}\right)}^2+{\left(\frac{x}{12}\right)}^2=1$$$$\frac{x^4+40x^2+400}{x^2}+x^2=144$$$$x^4-52x^2+200=0$$$$x^2=26+2\sqrt{119}$$$$\cos \varphi =\frac{{\left(\sqrt{2}x\right)}^2-4^2-6^2}{2\times 4\times 6}=\frac{x^2-26}{24}=\frac{\sqrt{119}}{12}$$$$\varphi ={\cos }^{-1}\frac{\sqrt{119}}{12}\approx 24.6°$$

Answered by Acem last updated on 08/Dec/22

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