# Deep Pit

Geometry Level pending

Underneath an ancient temple, archeologists found a deep, narrow pit. The three perfectly flat, polished sides they uncovered so far appeared to converge toward a point below. The edges of one of the sides made an angle of only $$10^\circ$$, the other $$15^\circ$$, and the last $$20^\circ$$. Deep down, resting against the sides of the pit, was a perfect sphere 20 centimeters in diameter. How far from the bottom of the sphere would be the end of the pit, if the walls continued to a point?