# if one vertex of an equilateral triangle of side "a" lies at origin and other lies on the line x=(square root of 3)*y the third vertex is..

Angle between the line and x axis is $tan\Theta =\sqrt{3}$, there fore using parametric equation we obtain othe coordinated as $(a/2,\sqrt{3}a/2)$.and third vertex will be on (a,0).