Triangle MNO is an equilateral triangle with sides measuring 16√3 What is the height of the triangle?

Each side of the triangle is 27.7128129211 and if you cut the triangle in half then you have a 30, 60, 90 triangle. The longest side is 27.7128129211 and your shortest side is 13.8564064606. when you go from the shortest side to the second longest side you multiply the shortest side by the square root of 3 to get the second longest side. Your answer is 24.0000000001