The radius of the cone is 3. The generatrix is inclined to the height at an angle of 30 degrees. Find the height.

there is such a property, in a triangle the side lying opposite an angle of 30 degrees is equal to half of the hypotenuse
We denote the height as x, which means the hypotenuse is 2x
Let’s compose the equation using the Pythagorean theorem.
9 + x ^ 2 = 4x ^ 2
3 ^ 2 = 9
x ^ 2 = 3
So the height is equal to the root of 3