Question

Find the length of a side of an equilateral triangle given its altitude is six inches long.

Answer 1

An equilateral triangle has three 60 degree angles.
The altitude divides it into two 30 60 90 triangles.
The altitude is the "middle side" of such a triangle.
When that is the case, the middle side divided by the square root of 3 = the short side and multiplied by (2/sq root (3)) equals the hypotenuse.
The hypotenuse is the side of the equilateral triangle. 
So, 6 * 2 / (sq root of 3) = 6.9282032303

Source:
http://www.1728.org/trig2.htm