This activity is intended to supplement Geometry, Chapter 8, Lesson 4.
Time required: 45 minutes
Topic: Right Triangles & Trigonometric Ratios
Calculate the trigonometric ratios for 45∘−45∘−90∘,60∘−60∘−60∘ and 30∘−60∘−90∘ triangles.
Teacher Preparation and Notes
This activity is designed to be used in a high school or middle school geometry classroom.
If needed, review or introduce the term median of a triangle. Any median of an equilateral triangle is also an altitude, angle bisector, and perpendicular bisector.
This activity is designed to be student-centered with the teacher acting as a facilitator while students work cooperatively.
The worksheet guides students through the main ideas of the activity and provides a place for students to record their work. You may wish to have the class record their answers on separate sheets of paper, or just use the questions posed to engage a class discussion.
To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
To download the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=7896 and select EQUIL and ISOSC.
Problem 1 – Investigation of Triangles
Would you have expected these segments to be equal in length?
Will they always be equal?
Problem 2 – Investigation of 30-60-90 Triangles
Measure the three sides of the triangle.
What do you notice about the three ratios?
Problem 3 – Investigation of 45-45-90 Triangles
Why do the ratios remain constant while the sides change?