Can some one help me with this.
A cone has a volume of 81 Pi cubic inches, and the vertx angle of the verticle cross section is 60 degrees. What is the height of the cone?
Although this doesn't use the length of the side directly, it's very convenient to draw a diagram of the cross section triangle, draw a line representing the height, then figure out formulas for the radius in terms of the side length and height in terms of the side length.
Once you have your r and h in terms of s, substitute them into the cone formula, solve for s.
Now that you have s, you can use your s-to-height formula and find the answer.