The lateral edge of a regular hexagonal pyramid is 14 and is inclined to the base plane at an angle of 60 degrees. Find the side of the base of the pyramid.
The side edge, the height of the pyramid and the radius of the circumscribed circle form a right-angled triangle. The angle between the height and the side edge is 30 degrees, therefore the radius of the circumcircle is equal to half of the lateral edge and is 7. The radius of the circumcircle is the side of an equilateral triangle, so the side of the base of the pyramid is 7.
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