how do i solve this problem "each side of an equilateral triangle measures 9cm.Find the height ,h,of the triangle

Question

Each side is 9cm and it an equilateral triangle ,so i need to find the height

Answer 1

the height divides one side in half and you have a right triangle

the height is the longer leg, the shorter leg is 9/2=4.5, and the hypotenuse is 9

using the Pythagorean Theorem...

9²=h²+(4.5)²

81=h²+20.25

81-20.25=h²

60.75=h²

h=√60.75

h=7.79 cm is the height

Answer 2

In an equilateral triangle, drop a vertical from the apex down to the midpoint of the base. You now have a 30-60-90 right triangle, with the hypotenuse being opposite the 90-degree angle you created when the vertical meets the base of the triangle. The hypotenuse (9 cm) in such a triangle is always 2/sqrt3 times longer than the height, so multiply your hypotenuse (9 cm) by squrt3/2 to get your height of 9(sqrt3/2) = 4.5 squrt3 = 7.79 cm.