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Question Number 198815 by a.lgnaoui last updated on 24/Oct/23

$$\mathrm{Determiner}\mathbf{x}$$

Commented by a.lgnaoui last updated on 24/Oct/23

Commented by cherokeesay last updated on 24/Oct/23

Commented by a.lgnaoui last updated on 24/Oct/23

$$\mathrm{exact}$$$$\mathrm{we}\mathrm{can}\mathrm{use}\mathrm{the}\mathrm{rectangle}\mathrm{triangle}$$$$\mathbf{ADB}$$$${\mathbf{DE}}^2=\mathbf{AE}\times \mathbf{EB}(\mathbf{DE}=\mathbf{x}+6)$$$${(\mathbf{x}+6)}^2=(\mathbf{R}+\mathbf{z}\cos \mathit{\alpha })(\mathbf{R}-\mathbf{z}\cos \mathit{\alpha })$$$$={\mathrm{R}}^2-{\mathbf{z}}^2\cos {}^2\mathit{\alpha }$$$$\sin \mathit{\alpha }=\frac{6}{\mathbf{z}}\cos {}^2\mathit{\alpha }=\frac{{\mathbf{z}}^2-36}{{\mathbf{z}}^2}$$$${\mathbf{R}}^2=64+{\mathbf{z}}^2$$$$\Rightarrow {\mathbf{x}}^2+12\mathbf{x}+36=64+36$$$${\mathbf{x}}^2+12\mathbf{x}-64=0\mathbf{x}=4$$

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