A section is drawn through the top of the cone at an angle of 600 to its base

A section is drawn through the top of the cone at an angle of 600 to its base. Find the distance from the center of the base of the cone to the section plane if the height of the cone is 12 cm.

The section of the cone is an isosceles triangle СDК, the height of which KM forms a linear angle ОМК equal to 60.

Then in a right-angled triangle KOM the angle OKM = (180 – 90 – 60) = 30.

The distance from the center of the circle to the plane of the section is the OH segment perpendicular to the height of the CM section of the CDM section.

Then the triangle ОHК is right-angled at point H.

The OH leg lies opposite the angle 30 of the OHK triangle, then OH = OK / 2 = 12/2 = 6 cm.

Answer: The distance from the center of the circle to the plane is 6 cm.