The height of an equilateral triangle equals I times the side length. Using I for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

1 answer

To find the height of an equilateral triangle, we can use the formula for the height \( h \) in terms of the side length \( s \):

\[ h = \frac{\sqrt{3}}{2} s \]

In this case, the side length \( s \) is given as 8 meters. Substituting this value into the formula gives:

\[ h = \frac{\sqrt{3}}{2} \times 8 \]

Now, calculate the height:

\[ h = 4\sqrt{3} \]

Since you mentioned using \( I \) for the square root of 3, we can substitute \( I \) in place of \( \sqrt{3} \):

\[ h = 4I \]

Now, to find the approximate height, we need to evaluate \( 4I \). The approximate value of \( \sqrt{3} \) is about \( 1.732 \). Therefore:

\[ h \approx 4 \times 1.732 = 6.928 \]

Therefore, the approximate height of the equilateral triangle with a side length of 8 meters is:

\[ \boxed{6.93} \text{ meters} \]