Three spheres of known centers and known radii intersect at 2 points.  This 
Excel 97 Worksheet calculates the 2 points:

http://www.geocities.com/jongiff2000/GPS_math.xls

Simply enter the coordinates of the 3 centers and 3 radii, and the Excel 
program calculates the coordinates of the 2 points instantly.

Save the Excel file if you'd like and use it for your applications.

For instance, suppose you have a tripod with two fixed legs and one 
adjustable leg.  The location of the vertex of the tripod can be calculated 
from the lengths of the 3 legs and the coordinates of their bases.

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A gunshot sends a bullet at Mach n sweeping out a cone of half angle c. 
Three microphones of known coordinates pick up the shock wave at known time 
differences.  From this information, what are the coordinates of the gunman? 
Find the trajectory of the bullet and predict where it will go before it 
gets there.

This problem has been solved and its solution is known and used on 
helicopters by the military.  Can you solve it?  I've tried and I can't. 
Find the vector equation, differentiate it with respect to time, and go from 
there.

A 4th microphone is used to determine if the gunshot originated from above 
or below the plane of the first 3.