The Sine Rule
Investigate ratios in triangles that are not right-angled
Students are able to drag the vertices of a triangle and see the effect on the size of each angle and the lengths of the opposite side. They then evaluate the ratios of side lengths to the sines of the opposite angles, and so discover the Sine Rule.
Finally they are led through a structured explanation of why the Sine Rule is true. It is left to the teacher to formalise the proof, and develop the techniques for finding missing sides and angles.
There is a 2-page student handout which gives detailed instructions of how to use the TI-Nspire document.