Three Lighthouses Problem*

The locations of three lighthouses A, B, and C are known on a map. You can measure the angle between the light beams coming from each pair of lighthouses.

Describe a procedure for determining your location on the map using the measures of these angles.


For example, on the map to the left, the location of some point on the water has angle of approximately 28 degrees between the rays from Lighthouse A and Lighthouse B and approximately 45 degrees between Lighthouse B and Lighthouse C. Where is that point?









Hint: This is a geometry problem

GSP file with map and sample angles.You can do constructions on top of the map.


*Adapted from

Polya, George (1962) Mathematical Discovery: On Understanding, Learning, and Teaching Problem Solving. Volume I. New York: John Wiley & Sons. Prob. 1.15, p. 16.