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?

**Image credit:** Wikipedia.

Round your answer to whole millimeters (that is 1 decimal place).

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