The height of an equivalent triangle equals square root of 3/2 times the side length using 7/4 for the square root of three what is the approximate height and meters of an equivalent triangle with a side length of 8 m

Answer 1

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

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

where \( s \) is the side length.

In this case, you provided the approximation for \( \sqrt{3} \) as \( \frac{7}{4} \) (which is approximately 1.75). The side length \( s \) is given as 8 m.

Now, substituting the values into the height formula:

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

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

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

Now, substitute back into the equation for \( h \):

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

This simplifies as follows:

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

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