RIGHT TRIANGLE TRIGONOMETRY OVERVIEW
Our eighth unit here in STEM Geometry Honors is possibly one of the most important in the entire year! Ratios that naturally exist in right triangles can be used to help identify similar triangles, and even be used to solve for missing sides and angles of triangles of different kinds! Throughout this unit we’ll build our knowledge of the six (6) most important trig functions: sin, cos, tan, csc, sec, cot.
Unit 8 is all about these main trig functions and how they get used in solving for the properties and measurements of right triangles. During this unit we’ll go through three major topics:
 Ratios within all right triangles and how those ratios are defined
 Measuring angles using degrees and using radians
 The functions sin, cos, tan and how to use them to solve triangles
 The functions csc, sec, cot and what they can do for us
 Inverse trig functions and how we use those to find missing angles
When you’re done, you’ll have covered the basics of right triangle trigonometry!
PART 1: TRIG RATIOS & ANGLES
(50 pts) About 3 days
The first part of our unit is all about the basics of right triangle trigonometry. We’ll start with an overview of the three main ratios that exist within all right triangles, and then we’ll give official names to each of them. We’ll also look at how angles are measured in triangles and we’ll make sure that we understand the degree and radian angle systems.
PART 2: SPECIAL RIGHT TRIANGLES
(60 pts) About 3 days
IN the second par of our unit, you’ll look into the details surrounding a special group of right triangles. Here you’ll investigate some of the key ratios that exist in these triangles, and use the ratios and proportions to solve more triangles. Then, we’ll look at some of the various applications of these special right triangles.
PART 3: MODEL IT!
(140 pts) About 3 days
Of course our unit will end with a review and test, but in addition you’ll get to build a model of similar figures! You’ll be asked to create a series of lasercut similar triangles. You’ll ethen use those triangles to compare their perimeters, areas, and volumes (weights) to better understand proportions in similar figures!
PART 1: Trig Ratios & Angles
Definitions of the basic trigonometric ratiosThe first part of this unit looks at definitions for the three main trig functions: sin, cos, tan. Each of these functions is simply a formal organization of the ratio between two carefully chosen sides of a triangle. These work well for us because if two right triangles are similar, then the ratio between corresponding sides will be equal. We can then take advantage of these common ratios to help identify similar triangles in different contexts. Using that, we’ll even be able to start with halfatriangle and use the ratios to solve for the missing half of the triangle.
GRADING & PROCESS
Use your engineering notebook and take a full page of notes on the three trig ratios. Make sure that your notes include pictures and details about how each ratio is defined!
Complete HW43: Tangent Ratio
Add to your notes about trig ratios as you keep working. Make sure to add at least one (1) example of all three trig ratios being used to solve triangles!
Complete HW44: Sine Ratio
Complete HW45: Cosine Ratio
Take Quiz 19: Trig Ratios
Trig Ratio Overview
Tangent
Sine
Cosine
What’s Due In Right Triangle Trigonometry Part1: Trig Ratios & Angles
 Notes on Tan, Sin, Cos
 HW43
 Trig Usage Notes
 HW44
 HW45
 Quiz 19: Trig Ratios
Here’s what’s due in Part 1: Trig Ratios & Angles
 Take notes on all three trig ratios: tan sin, cos
 Complete HW43: Tangent Ratio
 Next, add to your notes on trig ratios by including at least 1 example of how tan, sin, and cos are used!
 Complete HW44: Sine Ratio
 Complete HW45: Cosine Ratio
 Take Quiz 19: Trig Ratios
PART 2: Special Right Triangles
Using common ratios to define a set of special right trianglesThe second part of the unit looks at two very important “Special Right Triangles”. The Isosceles Right Triangle and the 306090 triangle are both super useful in math and engineering because they are relatively easy to identify, simple to work with, and can make solving triangles a trivial job. Your responsibility is to learn how to identify these two types of triangles, learn the ratios that describe their side lengths, and then get practice using these relationships in solving problems!
GRADING & PROCESS
Use your Engineering Notebook to take a full page of notes on the three presentations below about Special Right Triangles. Make sure that your notes include a detailed picture of the Right Isosceles and 306090 triangles.
Complete HW46: Special Right Triangles
Complete HW47: Special Right Triangle Applications
Complete HW48: TrigStar Practice 1
Take Quiz 20: Special Right Triangles!
Intro to Special Right Triangles
Right Triangle Details
More Right Triangles
What’s Due In Similarity Part 2: Special Right Triangles
 Special Triangles Notes
 HW46
 HW47
 HW48
 Quiz 20: Special Right Triangles
Here’s what’s due in Part 2: Special Right Triangles

Take notes on special right triangles, their ratios, and their definitions

Complete HW46: Special Right Triangles

Complete HW47: Special Right Triangle Applications
 Complete HW48: TrigStar Practice 1
 Take Quiz 18: Special Right Triangles
PART 3: Model It!
Create a lasercut series of modelsThe last part of our unit gives us the chance to build a series of lasercut similar triangles and investigate their properties to confirm both the functions of Autodesk Inventor as well as the mathematical relationships between similar shapes! First you’ll need to plan out your 4triangle series in your engineering notebook, and then build the proper triangles of various sizes within Autodesk Inventor. You’ll use the iProperties tab to record perimeter, area, and volume of each before exporting a .DXF file for use with the laser. After you’ve lasercut your 4 triangles, you’ll measure their perimeters, areas, and weights to see how these numbers compare to the values calculated by Autodesk. You’ll also get to compare these values to see what they tell use mathematically about similar figures.
Of course our unit will also end with a unit review, a chance to get questions answered, and our final unit test to wrap things up!
GRADING & PROCESS
Use your Engineering Notebook to make a plan for creating your customcut laser models.
Use Autodesk Inventor to create your triangles each of the proper size. Use the iProperties menu to record the perimeter, area, and volume of each of your four triangle models.
Export .DXF files of your triangles and cut them on the laser out of acrylic. Measure and record the perimeter, area, and weight of each of your four triangle models.
Compare your measured values to those calculated by Autodesk, and to investigate the relationships between similar figures
Complete the Unit 7 Review
Schedule time to talk with Benshoof and get questions answered
Take Unit Test 7: Similarity!
What’s Due In Similarity Part 3: Similar Laser Triangles!
 Triangle Plan
 Autodesk & iProperties
 Laser Cut
 Compare Triangles
 Unit 7 Review
 Question Time
 Unit 7 Test
Here’s what’s due in Part 3: Build It!
 Make a plan for creating your customcut laser models.
 Use Autodesk Inventor & iProperties to create your triangles each of the proper size
 Laser cut them out of acrylic & measure properties
 Compare your measured values to Autodesk, and investigate the relationships
 Complete the Unit 7 Review
 Schedule time to talk with Benshoof and get questions answered
 Take Unit Test 7: Similarity!