The height of an equilateral triangle equals square root of 3 over 2 times the side length. Using 7/4 for the square root of 3, what is the approximate height in meters of an equilateral triangle with a side length of 8 meters?

Answer 1

To find the height of an equilateral triangle with a side length of 8 meters, we can use the formula for the height \( h \) of an equilateral triangle in relation to its side length \( s \):

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

Substituting \( s = 8 \) meters into the formula, we have:

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

Given that we will use \( \sqrt{3} \approx \frac{7}{4} \), we can substitute this value into the equation:

\[ h = \frac{\frac{7}{4}}{2} \times 8 \]

First, simplify \( \frac{7}{4} \div 2 \):

\[ \frac{7}{4} \div 2 = \frac{7}{4} \times \frac{1}{2} = \frac{7}{8} \]

Now substitute this back into the height formula:

\[ h = \frac{7}{8} \times 8 \]

Next, calculate this multiplication:

\[ h = 7 \]

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

\[ \boxed{7} \text{ meters} \]