The triangle is a right angled triangle with [tex] B=90^o [/tex]. Now apply Pythagoras theorem,
[tex] hypotenuse^2=opposite^2 + adjacent^2 [/tex]
[tex] AB^2+BC^2=AC^2\\
x^2+6^2=\sqrt{117}^2\\
x^2+36=117\\
x^2=81\\
x=9
[/tex]
Thus, the value of [tex] x=9\;cm [/tex].
