Answer:[tex]FH=8\sqrt{51}[/tex]
Step-by-step explanation:
This is a special right triangle that has 30, 60 and 90 degress corners. Because it is a special triangle, it also has side length values which always consistent relationship with one another.
Side opposite the 30° angle: x
Side opposite the 90° angle: 2x
So, [tex]FG=8\sqrt{17}[/tex]
Then use Pythagorean theorem. [tex]c^{2} =a^{2} +b^{2}[/tex]
[tex](16\sqrt{17} )^{2} =FH^{2} +(8\sqrt{17} )^{2}[/tex]
[tex]FH^{2} =4352-1088[/tex]
[tex]FH=\sqrt{3264}[/tex]
[tex]FH=8\sqrt{51}[/tex]
