An equalateral has angles of 60 - 60 - 60
Drop a plumb line down from the vertex (hight point) that BISECTS the base.
Now you have TWO triangles of 60-30-90
You know the length of the shorter leg (it was a side BISECTED) and you know the HYPOTENUSE
Use pythag theorem to calculate the other LEG (which is the HEIGHT)
(you could also use law of sines etc)