Answer:
Step-by-step explanation:
Well you can't find the height of the cone using only the slant height because there simply isn't enough information
S = Slant Height
R = Radius
H = Height
However if you had the radius of the base of the cone, then you can use the Pytagorean theorem like so: H = square root(S^2 - R^2)
If you had the angle the slant made against the base, you could use:
H = S*sin(Angle)