The median of an equilateral triangle is 13 √3. Find a side of it.

1) Since the triangle is equilateral, then each of its angles will be equal to 60 degrees.

2) In an equilateral triangle, any median is both the height and the bisector. Therefore, the acute angle formed by the median dropped to the base of an equilateral triangle will be 60: 2 = 30 degrees.

3) Using the sine of 60 degrees, we find the side of the triangle:

sin (60) = 1 / (2 * 3 ^ (1/2)) = 13 * 3 ^ (1/2): X, where X is the desired side.

X = 13 * 3 ^ (1/2) * 2 * 3 ^ (1/2) = 13 * 2 * 3 = 78.

Answer: side length is 78.