The altitude bisects one of the lines of the equilateral triangle and makes an angle of 90 degrees at the intersection.
Let each side of the triangle be x, then: x^2 - (x/2)^2 = 15^2
x^2 - x^2/4 = 225
3x^2/4 = 225
3x^2 = 4 x 225 = 900
x^2 = 900/3 = 300
x = sqrt(300) ≈ 17.32