To find the height of an equilateral triangle given its side length, we can use the formula for the height \( h \):
\[ h = \frac{\sqrt{3}}{2} \times \text{side length} \]
Given that the side length is 8 meters and using the approximation \( \sqrt{3} \approx \frac{7}{4} \), we can substitute into the formula:
\[ h = \frac{7}{4} \times \frac{1}{2} \times 8 \]
Calculating step by step:
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First, calculate \( \frac{1}{2} \times 8 \): \[ \frac{1}{2} \times 8 = 4 \]
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Now multiply by \( \frac{7}{4} \): \[ h = \frac{7}{4} \times 4 = 7 \]
Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is 7 meters.