As the world becomes increasingly reliant on mobile technology, we have never been more connected. As a cell phone searches for a signal, its location is pinpointed and coordinated across a number of applications. Your precise location is used on a Google Map or even Facebook. Cell towers can determine how strong a signal is to a specific phone (i.e. how far away the phone is from the tower) and the general direction the phone is from the tower.
In geometry or precalculus class, this idea can be simplified to Law of Sines and the Law of Cosines problems. To date, thousands of criminal cases have been proven with forensic cell phone evidence. Since the world is a sphere and not a plane, this activity is only a simulation and a more simplified version of what professionals actually do (which they do with Spherical Geometry -- what for my advanced Calculus series! :-)
CAUTION: An answer key is provided, however rounding, as you know, can dramatically affect trigonometric functions so answers may be different. There are some ambiguous cases so you should answer the questions yourself to guide your students through their own problem solving.
In this 19 page document you will be given a mapping to the Content Standards, an outline for how to implement the project, and handout resources for students to use.
-- In “Triangulation”students will practice sketching diagrams and will attempt Law of Sines and Law of Cosines problems with three different initial conditions.
-- In “Forensics” students will engage in higher order thinking to develop strategies for using fictitious cell phone data. With each problem, students are asked to look at cell phone records and determine the locations of the cell phones using the Law of Sines and Law of Cosines.
-- In “Catch the Suspect” students will analyze the cell phone records of 4 suspects. Students will compare the locations of the phones with the known locations of the crimes. Students will use their results to determine which suspect is most likely to have committed the crime.
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