The height of an equilateral triangle equals 3 square root over 2 times thecide link uSing 7 over 4 for the √3.What is the approximate height in meters of an equal letter triangle with a side length of eight meters

1 answer

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

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

In this case, we are given that \( \sqrt{3} \) can be approximated as \( \frac{7}{4} \).

Now, substituting \( \frac{7}{4} \) for \( \sqrt{3} \) and the side length \( s = 8 \) meters:

\[ h = \frac{7}{4} \cdot \frac{1}{2} \cdot 8 \]

Calculating this step-by-step:

  1. First, simplify \( \frac{1}{2} \cdot 8 \): \[ \frac{1}{2} \cdot 8 = 4 \]

  2. Now, multiply by \( \frac{7}{4} \): \[ h = \frac{7}{4} \cdot 4 \]

  3. Simplifying this gives: \[ h = 7 \text{ meters} \]

Thus, the approximate height of the equilateral triangle with a side length of 8 meters is 7 meters.