You have a 30-60-90 triangle.
The ratio of the lengths of the sides of a 30-60-90 triangle is
[tex] 1 : \sqrt{3} : 2 [/tex]
The given side is the side whose length is between the other two .
It corresponds to sqrt(3) in the ratio.
[tex] HG = \dfrac{GI}{\sqrt{3}} [/tex]
[tex] HI = 2HG [/tex]
[tex] HG = \dfrac{GI}{\sqrt{3}} = \dfrac{11}{\sqrt{3}} = \dfrac{11 \sqrt{3}}{3} [/tex]
[tex] HI = 2HG = \dfrac{22 \sqrt{3}}{3}[/tex]
