The height of an equilateral triangle equals the 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?

1 answer

To find the height of an equilateral triangle given the side length, you can use the formula for the height \( h \):

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

where \( s \) is the side length. In this case, the side length \( s \) is 8 meters.

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

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

Calculating \( \frac{7/4}{2} \):

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

Now substitute this back into the height formula:

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

Now, when you multiply:

\[ h = 7 \text{ meters} \]

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

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