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

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