Nan’s art sculpture is a pyramid. She will cover all the faces with gems, except the base of the pyramid.
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By the law of cosines, the angle 
satisfies
which reduces to
which converts to approximately 77 degrees (this can be done my multiplying by 180 and dividing by pi).
which reduces to
which converts to approximately 77 degrees (this can be done my multiplying by 180 and dividing by pi).