hello
to solve this qiestion, we can either use pythagorean theorem or trigonometric ratio since it's a right angled triangle
but to save time, we can use pythagorean theorem
![\begin{gathered} 12^2=x^2+(6\sqrt[]{3})^2 \\ 144=x^2+108 \\ \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/v0rbud8bza3n8ug3qaskxeo369qmuk8u0q.png)
collect like terms
![\begin{gathered} x^2=144-108 \\ x^2=36 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/cwciy04kgm1fl1nvbabdvsjtubtyh3iyb0.png)
take the square root of both sides
![\begin{gathered} x^2=36 \\ x=\sqrt[]{36} \\ x=6 \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/d519qwfm87diz2c7jgebj4jzbly6z2grie.png)
from the calculations above, the value of x is equal to 6