From our diagram we can see that angle HED equals to angel GED and angle GDE equals to angel HDE.
Two triangles are similar if the corresponding angles are equal, so their corresponding sides will be in equal ratio.
Upon setting ratios of corresponding sides of our triangle equal we will get,
[tex]\frac{EG}{GD} =\frac{EH}{HD}[/tex]
[tex]\frac{99.2}{62} =\frac{112}{(x+2)}[/tex]
Now we will use cross multiplication to solve our equation,
[tex]99.2(x+2)=112\cdot 62[/tex]
[tex]99.2x+198.4=6944[/tex]
[tex]99.2x=6944-198.4[/tex]
[tex]99.2x=6745.6[/tex]
[tex]x=\frac{6745.6}{99.2}[/tex]
[tex]x=68[/tex]
Therefore, value of x will be 68 ft.
