Use interactive diagrams to investigate the ratio of two sides of a right-angled triangle.
The activity is a interactive introduction to the three trigonometric ratios: sine, cosine and tangent. There are separate diagrams for each.
Students can first drag a vertex of a right-angled triangle, changing the lengths of the sides but not the angles. Beneath the triangle there is a calculation that uses the measured lengths of two of the sides and they see that, no matter how the size of the triangle changes, the ratio of the two lengths remains the same.
Next they can use the slider to change an angle of the triangle. Now the ratio of the two lengths is different but, for any given angle, the ratio of two of the sides remains constant.
There is a series of multichoice questions to test students' understanding and, finally, the opportunity to create their own triangles, measure sides and angles, calculate ratios and confirm the connections that they have discovered.