To determine the length of the altitude of an equilateral triangle with side lengths of 8 units, follow these steps:
1. Identify the properties of an equilateral triangle:
An equilateral triangle has all three sides of equal length, and all three interior angles are 60 degrees.
2. Formula for the altitude of an equilateral triangle:
The altitude (height) of an equilateral triangle can be calculated using the formula:
[tex]\[
\text{altitude} = \frac{s \cdot \sqrt{3}}{2}
\][/tex]
where [tex]\( s \)[/tex] is the length of a side.
3. Plug in the side length into the formula:
Given the side length [tex]\( s = 8 \)[/tex] units, substitute [tex]\( s \)[/tex] in the formula:
[tex]\[
\text{altitude} = \frac{8 \cdot \sqrt{3}}{2}
\][/tex]
4. Simplify the expression:
Simplify the multiplication and division:
[tex]\[
\text{altitude} = 4 \cdot \sqrt{3}
\][/tex]
5. Result:
Therefore, the altitude of the equilateral triangle with side lengths of 8 units is:
[tex]\[
4 \cdot \sqrt{3} \approx 6.928203230275509
\][/tex]
The length of the altitude is approximately [tex]\( 6.928 \)[/tex] units. This number corresponds to the previously computed value using the given geometric properties and calculations.
