## flagpole.jpg - Section 3: Examples, Definitions, and Modeling

# Solving Right Triangle Trig Problems

Lesson 6 of 9

## Objective: SWBAT use trigonometric ratios and the Pythagorean Theorem to solve problems involving right triangles.

The opener is on the board as students enter the room:

**Two sides of a right triangle have lengths of 9 cm and 15 cm. **

**What is the length of the third side of this triangle? (There are two different solutions to this problem.)**

I give students a few minutes to work on the problem in their notebooks before asking for volunteers to put their solutions on the board. It's always interesting to see how quickly each student understands *why* there are two answers to this question. I am particularly interested in the students who wonder why there are not *three* solutions to this problem -- what would you tell them?

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We've spent the first five class periods of the semester working on the Similar Triangles Project. I spend a few minutes today reviewing the expecations for project submission, and the due date, which is coming up. As I visual, I project the project checklist at the front of the room, and I tell students to make sure that they're completing all parts of the project.

Also included here is a link the Google Form I use to debrief the Similar Triangles Project. I give students a few minutes of class time to complete this form during the first class after project due date.

#### Resources

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I have three straight-forward right triangle trig examples ready to go as practice problems today. There is nothing particularly special about these - you can substitute any of your favorites here.

The key is that when we work on these problems, I emphasize the idea of **modeling (MP4)**. Every time we read a problem in words, we're going to sketch a diagram of what it represents. With my students, I refer to this as the "easy part," and I make a show of it by saying, "If a problem says *right triangle*, what's the first thing I should do?" Along those same lines, we also pay attention to the idea that a model should be a simpler version of the reality it represents. On Example 3, I ask, "How should I draw a flagpole?" and what I want students to see is that my artistry doesn't really matter: I just need to draw a vertical line.

Once diagrams are sketched, I try to get students to think carefully about labeling them (**MP4, MP6**):

- What are we told in each of these problems?
- What are we trying to find?
- Where can I put the unknown?

After that, when it comes to definitions, the story is the same. We want to sketch diagrams of these words, because for many of us, it's easier to understand a diagram than a wordy definition. I talk about how each of these definitions is *precise* in its wording, and how sometimes, concise, precise wording of the sort you'll often find in mathematics can be dense and confusing. You have to read it slowly, and think carefully about exactly what it means. Drawing a diagram as you read is one way to do that.

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Since it is early in the semester I am quite careful about introducing the next assignment. U1 L6 explains how I go about it.

Once Trig Problem Set 3 and the new Delta Math Trig Ratio Exercises are introduced, I give students the rest of the period to work on these assignments. Some will choose to work on the Problem Set because they like having me and their classmates available to help, others will want to focus on Delta Math because this is the easiest place for them to access a computer. Whatever they choose, it's a nice, easy-going but hard-working vibe. I like to put on some music at times like this.

There is no formal closing or exit slip today, but I keep students updated about how much time is left in ten minute increments, and with 5 minutes left, I encourage them to record some next steps for what they'll work on tonight, and what they'll try to have done by the next time we meet.

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- UNIT 1: Statistics: Data in One Variable
- UNIT 2: Statistics: Bivariate Data
- UNIT 3: Statistics: Modeling With Exponential Functions
- UNIT 4: Statistics: Using Probability to Make Decisions
- UNIT 5: Trigonometry: Triangles
- UNIT 6: Trigonometry: Circles
- UNIT 7: Trigonometry: The Unit Circle
- UNIT 8: Trigonometry: Periodic Functions

- LESSON 1: Intro to Trigonometry / What is Similarity?
- LESSON 2: Course Structures and the Similar Triangles Project, Part 1
- LESSON 3: The Similar Triangles Project, Part 2: Empirical and Theoretical Data
- LESSON 4: Definitions of the Trig Ratios and a Fascinating Chart
- LESSON 5: Finishing Up the Similar Triangles Project
- LESSON 6: Solving Right Triangle Trig Problems
- LESSON 7: Constructing an Equilateral Triangle
- LESSON 8: Constructing Special Triangles on Geogebra
- LESSON 9: Using Special Right Triangles and Spotting Some Patterns