Question 753467
The picture shows enough information to indicate the smaller right triangle.  a is the longer leg of this small triangle and x is the hypotenuse of this small triangle.


Although I do not remember the official theorem, this smaller right triangle is also a 30-60-90 right triangle, similar to the main right triangle.


The other leg of this small right triangle is {{{x/2}}} in length.  
{{{a^2+(x/2)^2=x^2}}} directly according to pythagorean theorem
{{{x^2/4-x^2=-a^2}}}
{{{x^2-x^2/4=a^2}}}
{{{(1-1/4)x^2=a^2}}}
{{{x^2=(4/3)a^2}}}
{{{x=2a/sqrt(3)}}}
{{{highlight(x=(2/3)a*sqrt(3))}}} and you can substitute a=6 and evaluate x.