Title: (Investigation) Using Right Triangles to create Trig Ratios
Course: HBUHSD Geometry Resource Course > Section: Unit 5: Right Triangles and Trigonometric Ratios

Description: In this activity, groups of students are given an angle and are asked to draw some similar right triangles that include that angle. Students then measure the side-lengths of their triangles and find ratios of altitude/base, altitude/hypotenuse, and base/hypotenuse . Discussion about WHY the ratio is the same no matter what the size of the triangle will be essential for establishing the purpose of these values. The groups bring together their values and the class constructs a similar triangle ratio chart. This chart can be used to solve more precisely the hook activity or another problem like the Romeo and Juliet problem as presented in this post.

Teacher Description: Teachers must facilitate the learning environment.  Help collect the data on the sheet provided for the entire class (either using whiteboard, ELMO, Etc) Follow the open-ended style problem in the hook and provide another tool for students to use to solve that problem more precisely. Furthermore, the formal names for the trig values are purposefully omitted here to support conceptual understanding without bogging students down with heavy new vocabulary.

Student Description: Students are guided through an exploration of side length ratios of similar triangles and seeks to support them as they look for regularity in repeated reasoning.

Time: 25-30 minutes

Measuring Right Triangles .docx

Optional Classwork/Assignment:

Measuring Angles Homework.pdf