(Originais Teachy 2023) - Question Hard of Mathematics

A municipality is planning the construction of a new cultural space, which will be a modern cone-shaped pavilion with a height of 30 meters and a base radius of 20 meters. At the top of the cone, a special lighting will be installed that needs to be visible from a minimum distance of 1000 meters in all directions. Considering that the luminosity follows a uniform pattern and that the height of the pavilion is the reference for the visibility calculation, and knowing that the lighting at the top of the cone creates an opening angle of 60º, determine the maximum height at which an observer can be located and still be able to see the top of the pavilion. Disregard the curvature of the Earth and the influence of obstacles in the field of view and assume that the observer and the top of the cone are located on the same flat surface tangent to the ground.