Let's solve the problem step-by-step:
1. Identify the properties of an equilateral triangle: An equilateral triangle has all three sides of equal length and all interior angles of equal measure (60 degrees each).
2. Given information:
- The side length of the equilateral triangle is 18 inches.
3. Formula to find the height of an equilateral triangle:
- The height [tex]\( h \)[/tex] of an equilateral triangle can be determined using the formula:
[tex]\[
h = \frac{\sqrt{3}}{2} \times \text{side length}
\][/tex]
4. Substitute the given side length into the formula:
- Here, the side length is 18 inches:
[tex]\[
h = \frac{\sqrt{3}}{2} \times 18
\][/tex]
5. Simplify the expression:
- First, multiply the fraction:
[tex]\[
h = \frac{\sqrt{3} \times 18}{2}
\][/tex]
- Then, perform the multiplication:
[tex]\[
h = 9\sqrt{3}
\][/tex]
So, the height of the triangular base of the pyramid is [tex]\(\boxed{9\sqrt{3} \text{ inches}}\)[/tex].
