The radius of a circle circumscribed about a regular triangle is 18 find the height of this triangle.

A regular (equilateral triangle) is a triangle in which all sides are equal.
The radius of a circle circumscribed about a regular triangle is determined by the formula:
R = √3a / 3,
where a is the length of the side of the triangle.
Let’s find the length a:
√3a / 3 = 18;
a = 18 * 3 / √3 = 18 * 3 * √3 / 3 = 18√3 (conventional units).
In a regular triangle, all heights, bisectors and medians are found by the formula:
h = l = m = √3a / 2.
Let’s find the length of the height:
h = √3 * 18√3 / 2 = 18 * 3/2 = 9 * 3 = 27 (conventional units).
Answer: h = 27 conventional units.