How could I find the height of a truncated cone if I know the 2
sections and the taper of the cone

If you know the diameter of the top and bottom sections as well as the
taper in degrees, subtract the top (smaller) diameter from the bottom
and divide this result by two. If you look at the cone as a trapezoid
you'll see that by doing this you've gotten the base of one of the
triangles that form on either side. Now to find the height just use a
little geometry: assuming that the angle of the taper is from the
bottom to top of the cone (or what's actually called a frustrum)
multiply the value you found previously by the tangent of this angle.
Remember SOHCAHTOA? You're applying TOA here (tangent(angle) =
opposite/adjacent.

since i have no work i thot ill spend a LOT of time and answer it
diagramatically ;)


say this is your cone ABCD:

D           A
------------
\          /
 \        /
  \      /
   \    /
    ----
   C    B

let us look at half the cone :

       < -x -> 
          E  A
       ------
       |    /
       |   /
       |  /
       ---
	y B

say X is the RADIUS (DIAMETER DIVIDED BY 2) of the larger portion of the cone
and Y is the radius of the smaller portion


now you subtract y from x to get (X - Y). this will be de size of the
side of the triangle formed by connecting points A, B & E. Point E is
where a straight line from point B would meet the line AD.

Now we have a triangle ABE:


        X-Y
       E   A
       ----
       |  /
     H | /
       |/
       B

Let H be the height that we want to find that is length of EB. Let the
angle at B be Z. We already know this angle. Now Cosine of angle B
i.e. Z is length of EA divided by length of EB.

so u have : Cosine (Z) = (X-Y)/H

so H = (X-Y)/Cosine(Z)

oops so sorry ! Tangent of Z and NOT Cosine of Z = (X-Y)/H

so H = (X-Y)/Tangent(Z)

Thank you so much for the time and effort. This is very exaustive and
more than I ever expected.
Love Google !!!!!
Happy holidays,

Fabrizio

can u resolve the formula to find out the angle if you know height and sections?