30-60-90 and 45-45-90 Fun

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SWBAT identify trignometric relationships in right triangles with angle measurements of 30-60-90 degrees and 45-45-90 degrees.

Big Idea

Special delivery! Students discover ratios of side lengths in special right triangles by constructing squares and equilateral triangles.

Do Now

10 minutes

In this Do Now, students have an opportunity to apply their knowledge of trigonometry to a real-world problem  (MP 1).  There is no diagram included so students can choose to draw their own diagram or you might scaffold for students by drawing the diagram with them.  Further support for students might including prompting them first to identify which trigonometric ratio, sine, cosine or tangent might be used to solve the problem.

Discovery of 45-45-90 Triangles with Squares

30 minutes

Review of Triangle Constructions

5 minutes

Prior to completing the construction and discovery for 30-60-90 Triangle Construction and Discovery, you may need to review how to construct triangles with students.  This lesson provides scaffolded notes and websites which can be used as review tools.  Also, a quick review using this applet may help to remind students of how to construct equilateral triangles. 

Construction and Discovery for 30-60-90 Triangles

30 minutes

Activity/Homework and Exit Ticket

20 minutes

For an activity or homework assignment for this lesson, students can work on one of two websites focusing on special right triangles.  This website allows students to access questions that are focused on geometry-based questions, while this website has more trigonometry focused questions and applications (MP 1 and MP 8).  I like to assign both for homework, requiring that students show their work on a separate piece of paper, usually the geometry-focused website and the other website as bonus. 

The lesson exit ticket asks students to find the lengths of sides of a 30-60-90 triangle using the properties just learned.  You can scaffold this lesson by labeling each side length with the ratios for 30-60-90 or demonstrating how to find x first, and then asking students to find y on their own.