To find the height \( h \) of an equilateral triangle with side length \( s \), you can use the formula:
\[ h = \frac{\sqrt{3}}{2} s \]
You stated that the height equals \( 3\sqrt{2} \) times the side length, which is a different formula. Let's clarify the calculations for both cases:
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Using the original formula \( h = \frac{\sqrt{3}}{2} s \):
For \( s = 8 \) meters: \[ h = \frac{\sqrt{3}}{2} \times 8 \]
Using \( \sqrt{3} \approx 74/100 \) (or 0.74): \[ h \approx \frac{0.74}{2} \times 8 \approx 0.37 \times 8 \approx 2.96 \text{ meters} \]
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Using the altered form \( h = 3\sqrt{2} s \):
If we incorrectly use \( h = 3\sqrt{2} s \) instead, the calculation would yield: \[ h = 3\sqrt{2} \times 8 \] However, without a specific value for \( \sqrt{2} \) provided in your request, this calculation won't help us.
Since there is confusion in the information regarding which formula to use, based on the traditional formula is \( h = \frac{\sqrt{3}}{2} s \).
With the correct method, the approximate height of an equilateral triangle with a side length of 8 meters would be around 2.96 meters.
Let me know if you want the calculation with a specific value for \( \sqrt{2} \).
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