To find the height of an equilateral triangle given that the height equals \(3\sqrt{2}\) times the side length, we can use the following formula:
\[ \text{Height} = 3\sqrt{2} \times \text{side length} \]
Given that the side length of the triangle is 8 meters, we can substitute this value into the formula:
\[ \text{Height} = 3\sqrt{2} \times 8 \]
Now we can calculate the height:
\[ \text{Height} = 24\sqrt{2} \]
Next, we will use the approximate value of \(\sqrt{2}\):
\[ \sqrt{2} \approx 1.414 \]
Now we can calculate the height:
\[ \text{Height} \approx 24 \times 1.414 \]
Calculating that gives:
\[ \text{Height} \approx 33.936 \]
Therefore, the approximate height in meters of the equilateral triangle is:
\[ \text{Height} \approx 33.94 \text{ meters} \]
Thus, the final answer for the height of the equilateral triangle with a side length of 8 meters is approximately 33.94 meters.