To find the height of an equilateral triangle, we can use the formula for the height \( h \) in terms of the side length \( s \):
\[ h = \frac{\sqrt{3}}{2} s \]
In this case, the side length \( s \) is given as 8 meters. Substituting this value into the formula gives:
\[ h = \frac{\sqrt{3}}{2} \times 8 \]
Now, calculate the height:
\[ h = 4\sqrt{3} \]
Since you mentioned using \( I \) for the square root of 3, we can substitute \( I \) in place of \( \sqrt{3} \):
\[ h = 4I \]
Now, to find the approximate height, we need to evaluate \( 4I \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \). Therefore:
\[ h \approx 4 \times 1.732 = 6.928 \]
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is:
\[ \boxed{6.93} \text{ meters} \]