Students will derive the Law of Cosines by collecting and observing data.

Students will observe relationships in a triangle with two fixed sides (‘a’ and ‘b’), their included angle, and a third side (‘c’) in a triangle.  They will then observe the data collection and animation relating the measure of the included angle between the two fixed sides and the value of the expression a² + b² – c² for the triangle (where ‘a’ and ‘b’ are the fixed sides) for the given angle.  The data collected will present a familiar trig function that students will work with to develop the Law of Cosines.