To find the height of an equilateral triangle given the side length, you can use the formula for the height \( h \):
\[ h = \frac{\sqrt{3}}{2} \times s \]
where \( s \) is the side length. In this case, the side length \( s \) is 8 meters.
Given that we will use \( \sqrt{3} \approx \frac{7}{4} \), we can substitute this into the formula:
\[ h = \frac{7/4}{2} \times 8 \]
Calculating \( \frac{7/4}{2} \):
\[ \frac{7/4}{2} = \frac{7/4}{2/1} = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \]
Now substitute this back into the height formula:
\[ h = \frac{7}{8} \times 8 \]
Now, when you multiply:
\[ h = 7 \text{ meters} \]
Thus, the approximate height of the equilateral triangle with a side length of 8 meters is:
\[ \boxed{7 \text{ meters}} \]