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Question Number 183236 by a.lgnaoui last updated on 23/Dec/22

$$dererminerlavaleurx?$$

Commented by a.lgnaoui last updated on 23/Dec/22

Commented by mr W last updated on 24/Dec/22

$$‘‘\mathit{p}\mathit{a}\mathit{r}{\mathit{m}\mathit{e}\mathit{s}\mathit{u}\mathit{r}\mathit{e}}^{″}\mathit{m}\mathit{e}\mathit{t}\mathit{h}\mathit{o}\mathit{d}$$$$x=9$$$$howigot?$$$$imeasuredwitharuler.$$

Answered by mr W last updated on 24/Dec/22

$$say\alpha =\mathrm{\angle }DCB$$$$10\tan \alpha +10\sin \alpha =10$$$$\Rightarrow \tan \alpha +\sin \alpha =1$$$$lett=\tan \frac{\alpha }{2}$$$$\Rightarrow \frac{2t}{1-t^2}+\frac{2t}{1+t^2}=1$$$$\Rightarrow t^4+4t-1=0$$$$\Rightarrow t=\frac{\sqrt{2\sqrt{2}-1}-1}{\sqrt{2}}$$$$\cos \alpha =\frac{1-t^2}{1+t^2}=\frac{\sqrt{2}-1+\sqrt{2\sqrt{2}-1}}{2}$$$$x=10\cos \alpha =5(\sqrt{2}-1+\sqrt{2\sqrt{2}-1})\approx 8.832$$

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