This is an investigation where students discover the ratios of sine, cosine and tangent in relation to right triangles. I use this with my high school geometry class before they have any idea what those sin, cos, and tan buttons mean on their calculator. Its a fun activity to lead them to discovering the ratios for themselves!
Make sure to go over the directions with the class and point out an example of what sides would be the opposite, hypotenuse, and adjacent sides. Students complete the inquiry with a 30-60-90 triangle but then are asked if they think it works with all right triangles. They are then encouraged to create their own right triangle and see if it still works.
Students love this investigation and a lot of aha moments come from it. Note that students need to be precise as possible and round answers out to 3-4 decimals in order to see the patterns.
I often use this as a test to assess students' ability to investigate patterns as well.