Answer:
20√3/3 or approx. 11.55 in.
Explanation:
Draw an equilateral triangle with one height to one side.
The height divides the triangle into two congruent right triangles.
At the vertex where the height is, each angle of the small triangles is 30 deg.
The other acute angle of the right triangle measures 60 degrees.
The two right triangles are 30-60-90 right triangles.
The ratio of the lengths of the sides of a 30-60-90 right triangle is
1 : √3 : 2
The height is opposite the 60-deg angle, so it corresponds to the side with length √3 in the ratio.
The long leg measures 10.
The short leg measures 10/√3 = 10√3/3
The hypotenuse measures 20√3/3
The side of the equilateral triangle is the hypotenuse of each small right triangle.
Answer: 20√3/3 or approx. 11.55 in.