The Cosine Rule (Law of Cosines)

Investigating the Cosine Rule (Law of Cosines) for non-right-angled triangles, and formulas for calculating their areas.

Author and programmer: Ron Barrow

UK Years 10-12, KS4, KS5, Higher GCSE Mathematics, Grades A - A* - Shape, Space and Measure
US - Grades 10-12 - Geometry


Instructions below    See also: The Sine Rule   PRINT

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How to Use this Applet

This program aims to help you to use the Cosine Rule for finding angles and side-lengths in triangles which are not right-angled.
The triangle on the screen can be move around by clicking and dragging its vertices, which are marked with small red circles.
At the top of the screen you can check the box next to the "Working" label if you want to see the working calculations that are done using the Cosine Rule.
At the bottom of the screen you can use the buttons to check whether you want to find side-lengths a, b, c, or angles A, B, C.

Whatever you chose to find the Cosine Rule is the same but is rearranged to perform the different calculations. You'll get a good feel for the way the rule works by playing around and seeing what happens.
If you are also interested in calculating the areas of the triangles as you draw them, then check the "Areas" box. There are two formulae used for this, depending on what measures you already know. Once again, play around. Good luck!