Respuesta :

sam4040

Answer:

[tex]X=12-6\sqrt{3}=1.6077[/tex]

Step-by-step explanation:

Given that [tex]Y=6[/tex]

[tex]\tan(75)=\frac{Y}{X} \\X=\frac{Y}{\tan(75)}=Y\cot75=6\cot75 \\\\Calculate \ \cot(75)\\\tan(75)=\tan(45+30)=\frac{\tan45+\tan30}{1-\tan45 \cdot \tan30} =\frac{1+\frac{1}{\sqrt{3} } }{1-\frac{1}{\sqrt{3} } } \\\tan75=\frac{\sqrt{3}+1 }{\sqrt{3}-1 } =2+\sqrt{3} \\\cot75=\frac{1}{2+\sqrt{3} } =\frac{2-\sqrt{3} }{2^2-3} =2-\sqrt{3} \\\\Hence\\X=6\cot75=6 \cdot(2-\sqrt{3})\\X=12-6\sqrt{3} \approx1.6077[/tex]

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