The height of the cone is 20, and the length of the generatrix is 29, find the diameter of the base of the cone.

Since the height of the cone is perpendicular to its base, the height of the cone, its generatrix and the radius of the base make up a right-angled triangle. The hypotenuse of this triangle will be the generatrix of the cone, and the legs will be the height of the cone and the radius of the base.
Let’s say the base radius is r.
Using the Pythagorean theorem, we get the equation:
r2 + 202 = 292,
r2 = 292 – 202,
r2 = 841 – 400 = 441,
r = 21.
If the radius of the base is 21, then its diameter, respectively, is 2 * r = 42.
Answer: d = 42.