To determine the height of the triangular base of the pyramid, we will analyze the properties of an equilateral triangle. An equilateral triangle has all three sides of the same length and all three angles equal to 60 degrees.
Given:
- Base edge length of the equilateral triangle is 18 inches.
We need to find:
- The height of this equilateral triangle.
The formula for the height ([tex]\( h \)[/tex]) of an equilateral triangle with side length [tex]\( a \)[/tex] is given by:
[tex]\[ h = \frac{a \sqrt{3}}{2} \][/tex]
Here, [tex]\( a = 18 \)[/tex] inches.
Let's substitute [tex]\( a \)[/tex] into the formula to find [tex]\( h \)[/tex]:
[tex]\[ h = \frac{18 \sqrt{3}}{2} \][/tex]
[tex]\[ h = 9 \sqrt{3} \][/tex]
So, the height of the triangular base is:
[tex]\[ 9 \sqrt{3} \][/tex]
From the given options:
1. [tex]\( 9 \sqrt{2} \)[/tex]
2. [tex]\( 9 \sqrt{3} \)[/tex]
3. [tex]\( 18 \sqrt{2} \)[/tex]
4. [tex]\( 18 \sqrt{3} \)[/tex]
The correct option is:
[tex]\( 9 \sqrt{3} \)[/tex] inches.
Thus, the height of the triangular base of the pyramid is [tex]\( 9 \sqrt{3} \)[/tex] inches, which corresponds to option 2.
