Side ratios of similar triangles
Understand that, due to properties of similar triangles, side ratios in right triangles are properties of the angles in the triangle.
After an open-ended task intended to motivate the need for trigonometric ratios (although the term is not used), students examine side ratios of similar right triangles. Students then build tables of side ratios for several similar triangles while noting that quotients of corresponding sides are the same. Using their knowledge of similar triangles they see that the ratios are a property of an angle rather than of a triangle. Only after laying this groundwork do students learn that, for right triangles, the ratios are called “sine,” “cosine,” and “tangent.” Finally, students examine the relationship between sine and cosine and use this knowledge to solve a variety of problems.