Investigating Right Triangle Trigonometry
Summary
Students will use a hands-on approach to investigate how scaling a triangle does not affect the trig definitions and ratios based on that triangle. Students measure legs in a triangle unique to them, compute the hypotenuse, and find the six trig ratios of an angle. Students then compare results with group members that have similar triangles on a larger or smaller scale. Students are asked to draw conclusions at different points throughout the activity.
Students also use their knowledge of trig ratios to solve right triangles given an angle and a side.
Learning Goals
Students learn the definitions of six trig function ratios.
Students learn that trig definitions are independent of the scale of the triangle, and depend only on the angle.
Students solve right triangles for missing sides given an angle and one side.
Students learn that trig definitions are independent of the scale of the triangle, and depend only on the angle.
Students solve right triangles for missing sides given an angle and one side.
Context for Use
This is designed for a 50 min. class with 10-15 min being an instructor "mini-lecture introduction" and 35-40 min of students working through the activity.
Appropriate for college or high school course that includes right triangle trigonometry. Activity assumes groups of 3-4 students working together.
Can be used as an introduction or for reinforcement.
Appropriate for college or high school course that includes right triangle trigonometry. Activity assumes groups of 3-4 students working together.
Can be used as an introduction or for reinforcement.
Description and Teaching Materials
Students are given a brief introduction to right triangle definitions and must measure and compute trig ratios for their own triangle. Students then make comparisons with their group members and are led through a series of questions getting them to think critically and form conclusions based on what they have found.
Students also solve a series of problems finding missing lengths of right triangles given an angle and a side.
Teachers will need to print out the "Right Triangle Trigonometry Definitions" file and copy the appropriate pages for the student activity.
Teachers also copy and cut out the triangles included in the file.
Instructor notes are also included in the first page of the file.
Rulers (with cm) and calculators will also be necessary for the activity. Right Triangle Trig Definitions (Microsoft Word 2007 (.docx) 95kB Dec9 16)
Right Triangle Trig Definitions (Acrobat (PDF) 411kB Dec9 16)
Students also solve a series of problems finding missing lengths of right triangles given an angle and a side.
Teachers will need to print out the "Right Triangle Trigonometry Definitions" file and copy the appropriate pages for the student activity.
Teachers also copy and cut out the triangles included in the file.
Instructor notes are also included in the first page of the file.
Rulers (with cm) and calculators will also be necessary for the activity. Right Triangle Trig Definitions (Microsoft Word 2007 (.docx) 95kB Dec9 16)
Right Triangle Trig Definitions (Acrobat (PDF) 411kB Dec9 16)
Teaching Notes and Tips
Special notes are included in the file.
You should make sure students are not measuring the hypotenuse of the triangle, but rather computing it with the pythagorean theorem and using the exact value.
You should make sure students are not measuring the hypotenuse of the triangle, but rather computing it with the pythagorean theorem and using the exact value.
Assessment
Student effort and completion of the activity is most appropriate. A 0-5-10 scale with 10 being complete with few to no errors, 5 being incomplete or complete but with several errors, and 0 being no to little of the assignment completed.