The Law of Cosines

We start with 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: . Show Cuoco's theorem by clicking on the checkbox.
  • Drag the slider to rearrange the square with area .
The Law of Cosines is a generalization of the Pythagorean theorem. Click on the Right triangle checkbox to see this. Drag the vertices of the triangle to see different configurations. This applet is based on the article “The Cuoco Configuration” by Roger E. Howe, The American Mathematical Monthly, Vol. 120, Dec. 2013, 916- 923.