To find the height of an equilateral triangle with a side length of 8 meters, we use the formula for the height (\( h \)) of an equilateral triangle, which is given by:
\[ h = \frac{\sqrt{3}}{2} \times s \]
where \( s \) is the side length of the triangle.
We are given that the side length \( s = 8 \) meters. We're also using \( \frac{7}{4} \) as an approximation for \( \sqrt{3} \).
Substituting the values into the formula, we get:
\[ h = \frac{7}{4} \times \frac{1}{2} \times 8 \]
Calculating the factors step by step:
- First, calculate \( \frac{1}{2} \times 8 = 4 \).
- Next, multiply \( \frac{7}{4} \) by \( 4 \):
\[ h = \frac{7}{4} \times 4 = 7 \]
Thus, the approximate height of the equilateral triangle with a side length of 8 meters is:
\[ \boxed{7 \text{ meters}} \]