To find the height of an equilateral triangle given that the height \( h \) is equal to \( \sqrt{3} \) times the side length \( s \), we can use the formula:
\[ h = \frac{\sqrt{3}}{2} s \]
In this case, the problem states that the height equals \( 3\sqrt{2} \) times the side length. Therefore, our equation becomes:
\[ h = 3\sqrt{2} \cdot s \]
Given \( s = 8 \) meters, we substitute:
\[ h = 3\sqrt{2} \cdot 8 \] \[ h = 24\sqrt{2} \]
It is provided that \( \sqrt{2} \) is approximately \( 74 \). However, this value appears to be incorrect (it likely refers to a numerical approximation, not a square root).
Knowing that \( \sqrt{2} \approx 1.414 \), we can calculate:
\[ h \approx 24 \cdot 1.414 \] \[ h \approx 33.936 \]
Thus, the approximate height of the equilateral triangle with a side length of 8 meters is approximately \( 33.94 \) meters.
If we were to use a hypothetical value where \( \sqrt{3} \) represents \( 7 \) or \( 74 \) (seemingly a miscommunication), then adjustments could be made accordingly.
Consequently, assuming \( \sqrt{2} \) is meant, the answer is:
Approximately 33.94 meters.
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