To find the height of an equilateral triangle when you know the side length, you can use the formula for the height \( h \) of an equilateral triangle:
\[ h = \frac{\sqrt{3}}{2} \times s \]
where \( s \) is the side length.
In this case, the side length \( s \) is 8 meters. You mentioned that the height equals \( 3\sqrt{2} \) times the side length. However, it appears there may be some inconsistency because the height of the equilateral triangle is typically given as proportional to \( \sqrt{3} \).
Nevertheless, let’s calculate the height using both interpretations(3√2 and the standard formula).
-
Using \( 3\sqrt{2} \) times the side length: \[ h = 3\sqrt{2} \times 8 = 24\sqrt{2} \] We will calculate \( h \) using an approximate value of \( \sqrt{2} \) (approximately 1.414): \[ h \approx 24 \times 1.414 \approx 33.936 \text{ meters} \]
-
Using \( \frac{\sqrt{3}}{2} \) times the side length: \[ h = \frac{\sqrt{3}}{2} \times 8 = 4\sqrt{3} \] Now we substitute \( \sqrt{3} \) with 74: \[ h \approx 4 \times 74 = 296 \text{ meters} \]
If we based it on \( 3\sqrt{2} \), the height would be approximately 33.936 meters, while using the traditional formula with your value of \( \sqrt{3} \) would result in approximately 296 meters.
Please verify the specifics of the problem for clarity on which height calculation you require.
8 answers