Answer :
Sure! Let's solve the problem step-by-step to find the length of the altitude of an equilateral triangle with side lengths of 8 units.
### Step 1: Understanding the equilateral triangle
An equilateral triangle is a triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.
### Step 2: Finding the altitude
The altitude of an equilateral triangle can be found using a known geometric formula.
### Step 3: Formula for the altitude
The altitude (\(h\)) of an equilateral triangle with side length (\(a\)) is given by:
[tex]\[ h = \frac{\sqrt{3}}{2} \times a \][/tex]
### Step 4: Plug in the given side length
Given the side length (\(a\)) is 8 units:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 8 \][/tex]
### Step 5: Simplifying the expression
[tex]\[ h = 4 \sqrt{3} \][/tex]
### Step 6: Calculating the numerical value (Given answer)
The numerical value of \(4 \sqrt{3}\) is approximately:
[tex]\[ h \approx 6.928203230275509 \][/tex]
Therefore, the length of the altitude of the equilateral triangle is approximately 6.928 units.
### Step 1: Understanding the equilateral triangle
An equilateral triangle is a triangle in which all three sides are equal in length, and all three angles are equal to 60 degrees.
### Step 2: Finding the altitude
The altitude of an equilateral triangle can be found using a known geometric formula.
### Step 3: Formula for the altitude
The altitude (\(h\)) of an equilateral triangle with side length (\(a\)) is given by:
[tex]\[ h = \frac{\sqrt{3}}{2} \times a \][/tex]
### Step 4: Plug in the given side length
Given the side length (\(a\)) is 8 units:
[tex]\[ h = \frac{\sqrt{3}}{2} \times 8 \][/tex]
### Step 5: Simplifying the expression
[tex]\[ h = 4 \sqrt{3} \][/tex]
### Step 6: Calculating the numerical value (Given answer)
The numerical value of \(4 \sqrt{3}\) is approximately:
[tex]\[ h \approx 6.928203230275509 \][/tex]
Therefore, the length of the altitude of the equilateral triangle is approximately 6.928 units.
