May 14, 2015

In this and the next lesson, students discover that the values of the sine and cosine ratios in a right triangle depend solely on the measure of the acute angle by which the adjacent, opposite, and hypotenuse sides are identified. To do this, students first learn how to identify these reference labels. Then, two groups take measurements and make calculations of the values of the and ratios for two sets of triangles, where each triangle in one set is similar to a triangle in the other. This exploration leads to the conclusion regarding the “incredibly useful ratios.”

- Mathematics > General
- Mathematics > Geometry

- Grade 9
- Grade 10

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use of structure.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.