The height of an equilateral triangle equals square root 3/2 times the side length. Using 7/4 for the square root 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

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:

1. First, calculate \( \frac{1}{2} \times 8 = 4 \).
2. 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:

\[
\boxed{7 \text{ meters}}
\]