Stephanie Conklin SARATOGA SPRINGS HIGH SCHOOL, SARATOGA SPRINGS, NY
Geometry : Unit #11 - Trig Trickery : Lesson #4

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

Objective: SWBAT identify trignometric relationships in right triangles with angle measurements of 30-60-90 degrees and 45-45-90 degrees.
Standards: 8.G.B.7 HSG-SRT.C.6 MP1 MP8
Subject(s): Math
60 minutes
1 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.

2 Discovery of 45-45-90 Triangles with Squares - 30 minutes
Discovery for 30-60-90 and 45-45-90 Fun Video Narrative.wmv
https://betterlesson.com/lesson/section/27940/30-60-90-and-45-45-90-fun
3 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.

4 Construction and Discovery for 30-60-90 Triangles - 30 minutes
5 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.