The length of the altitude, or the value of variable "a", is
.
The triangle made up by the altitude, the left side of the whole triangle, and the segment whose endpoints are the bottom left vertex and the point of intersection between the altitude and side is a 30-60-90 triangle. Triangles with these angles have a certain ratio that their sides must follow. The hypotenuse is always twice as long as the shorter leg, and the longer leg is always
radical 3 as long as the shorter leg. The length of the shorter leg in this example is 4, therefore the altitude (or the longer leg) must be