We know that in a right triangle the cossine of an angle if giving by the formula:
[tex]\cos (\alpha)=\frac{adjacent}{Hypotenuse}[/tex]
We also know that:
[tex]\cos (30\degree)=\frac{\sqrt[]{3}}{2}[/tex]
Using those information in our triangle, we find:
[tex]\cos (30\degree)=\frac{12}{Hypotenuse}\text{ }\Rightarrow\text{ }\frac{\sqrt[]{3}}{2}=\frac{12}{Hypotenuse}\text{ }\Rightarrow\text{ }Hypotenuse=\frac{12\times2}{\sqrt[]{3}}[/tex]
Continuing with the algebra, we find:
[tex]Hypotenuse=\frac{24}{\sqrt[]{3}}\times\frac{\sqrt[]{3}}{\sqrt[]{3}}\text{ = }\frac{24\sqrt[]{3}}{3}\text{ = 8}\sqrt[]{3}[/tex]
So, our Hypotenuse is:
[tex]Hypotenuse\text{ = 8}\sqrt[]{3}[/tex]
