Lami's Theorem / Sine Rule

This is an interactive Geogebra page. I use it for teaching CAIE Mechanics (M1).

You can run this page in a browser by clicking here or you can download the file if you want to. Geogebra pages can easily be embedded into other web-sites, including Firefly.

You can click-and-drag the spots marked A, B and C to change the triangle of forces and the force diagram on the left will adjust itself to match.

I hope the controls are fairly self-explanatory, but get in touch with me if you have a suggestion.

You can use it to represent any equilibrium situation with only three forces. The examples I tend to use are:

• three students fighting over a Take That CD (or whatever) pulling in different directions
• a box at rest on a rough slope

Perhaps you can think of a suitable non-example to include - a cyclist going up a hill, say? Too many forces to consider using a triangle of forces. Another non-example which is not equilibrium maybe?

Anyway, once the class is comfortable that a triangle of forces means equilibrium, then Lami’s theorem and the Sine Rule can be shown to be equivalent. Maybe you could challenge your students to convince you that they are equivalent, but they are not allowed to use any trig identities, or you insist they have to refer to the graph of sine in their explanation.