The Law of CosinesWe start with an acute triangle ABC and construct a square on each side. The altitudes of the triangle extended to the opposite sides of the corresponding squares cut each square in two rectangles. Use the GeoGebra applet below to demonstrate the Law of Cosines: $c^2=a^2+b^2 – 2ab \cos(\gamma)$. This applet is based on the article “The Cuoco Configuration” by Roger E. Howe, The American Mathematical Monthly, Vol. 120, Dec. 2013, 916 923. 

Irina Boyadzhiev, Created with GeoGebra Dec. 6, 2013