To find the height of an equilateral triangle, we can use the formula for the height \( h \) of an equilateral triangle in terms of its side length \( s \):
\[ h = \frac{\sqrt{3}}{2} s \]
In this case, we are given that \( \sqrt{3} \) can be approximated as \( \frac{7}{4} \).
Now, substituting \( \frac{7}{4} \) for \( \sqrt{3} \) and the side length \( s = 8 \) meters:
\[ h = \frac{7}{4} \cdot \frac{1}{2} \cdot 8 \]
Calculating this step-by-step:
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First, simplify \( \frac{1}{2} \cdot 8 \): \[ \frac{1}{2} \cdot 8 = 4 \]
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Now, multiply by \( \frac{7}{4} \): \[ h = \frac{7}{4} \cdot 4 \]
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Simplifying this gives: \[ h = 7 \text{ meters} \]
Thus, the approximate height of the equilateral triangle with a side length of 8 meters is 7 meters.