To solve for the height of an equilateral triangle with a base edge length of 18 inches, let's follow a step-by-step approach.
1. Understanding the Equilateral Triangle:
- An equilateral triangle has all three sides of equal length.
- The height of an equilateral triangle splits the base into two equal halves and forms two 30-60-90 right triangles.
2. Using the 30-60-90 Triangle Properties:
- In a 30-60-90 triangle, the ratio of the sides opposite the 30°, 60°, and 90° angles is 1 : [tex]\( \sqrt{3} \)[/tex] : 2.
- If the full base of the equilateral triangle is 18 inches, each half of the base is [tex]\( \frac{18}{2} = 9 \)[/tex] inches.
3. Calculating the Height:
- In a 30-60-90 triangle, the height (opposite the 60° angle) is given by the length of the side opposite the 30° angle (which is 9 inches, half of the base length) times [tex]\( \sqrt{3} \)[/tex].
[tex]\[
\text{Height} = 9 \times \sqrt{3}
\][/tex]
4. Conclusion:
- Thus, the height of the equilateral triangle with a base edge length of 18 inches is [tex]\( 9\sqrt{3} \)[/tex] inches.
This matches one of the given choices. Therefore, the correct answer is:
[tex]\[ 9 \sqrt{3} \text{ in} \][/tex]
