# Trigonometry in Right Triangles

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 Keywords: Geometry, Right Triangles, Trigonometry Subject(s): Geometry Grades 9 through 10 NETS-S Standard: Creativity and InnovationCritical Thinking, Problem Solving, and Decision MakingTechnology Operations and ConceptsView Full Text of Standards School: Johnson-Brock Jr Sr High School, Johnson , NE Planned By: Ryan Zuhlke Original Author: Ryan Zuhlke, Johnson
Geometry - Section 8.3 – Prentice Hall Series

Trigonometry in Right Triangles

This lesson follows a combination of the Madeline Hunter lesson plan template and the gradual release of responsibility approach as introduced by Pearson and Gallagher.

Instructor: Mr. Zuhlke

Date and Time: (insert as needed)

Number of Students: (insert as needed)

Objectives:
• TLW (the learner will) effectively demonstrate understanding of how trigonometry works with right triangles.
• TLW correctly use trigonometric ratios to determine side lengths and angles measures in right triangles.

Standards:
• MA 11.3.1 Characteristics: Students will identify and describe geometric characteristics and create two- and three-dimensional shapes.
• MA 11.3.1.d Identify and apply right triangle relationships including sine, cosine, and tangent.
• MA 11.3.1.e Create geometric models to visualize, describe, and solve problems using similar triangles, right triangles, and trigonometry.

Materials Needed
Teacher: Note taking guides with necessary vocabulary and pre-determined examples as well as technology materials outlined below.
Students: Writing utensil, calculators, and books.

Technology
I will distribute my self-created note-taking guides for the students to use. Using my laptop, SmartBoard, a handheld marker board, and IPEVO Mirror-Cam I will have everything I need to project the instructional input content and examples we work through to students. Students know they are to write essentially everything I do and any additional notes they want for themselves. The handheld marker board will be on my laptop keypad and the Mirror-Cam will project this to the SmartBoard.

Anticipatory Set:
To begin the lesson, I will ask the kids to summarize what they have previously learned or know about right triangles and special right triangles (45-45-90 and 30-60-90). This is the content from the first two sections in Chapter 8. As an intro to the day’s lesson, I will ask the class if they had ever heard of the phrase SOH CAH TOA or Sine, Cosine, or Tangent. I would expect for some to have at least had some encounter with this content through previous MAP tests or elsewhere. This will be the primary basis for the day’s lesson, and this serves as a quick way for me to assess the students’ exposure to trig functions.

Objective and Purpose (articulated to the students)
(I will start by stating the objectives from above) Today as a class we are going to learn how trigonometry can help us when looking at right triangles that are not special right triangles. Trigonometry is a new concept for most of us and will be vital as all of you move forward through your school years and can have a variety of applications in your real-world, everyday lives. As you know, this entire chapter is focused on right triangles, and trigonometry plays a major role in them. The objectives that we discussed will help us meet several standards that have been set by the state for Geometry on which you will be assessed your junior.

Instructional Input/Modeling
Following the anticipatory set and objective and purpose, we will move into the nuts and bolts of the lesson. The first thing I will do is write SOH CAH TOA on the marker board and explain and write what each one means and when each one should be used to find a side length. I will start with a generic right triangle and instruct how to identify the adjacent side of an angle of interest vs the opposite side. The hypotenuse, as they know, is always across from the right angle and is the longest side. We will work on creating our ratios from this triangle. I will then work through at least one equation problem of each: Sine, Cosine, and Tangent. We will use these to find missing side lengths and then will use the inverse of each trig function to find missing angle measures. If they seem to understand what is going on with the process, I will move forward to Guided Practice. If not, I will do another problem that involves each trigonometric function.

Guided Practice and Monitoring
I will move to this point once the students seem to be grasping the new content. The responsibility will now be on their shoulders to solve the new problems that I present. I will strategically select students to decide which one needs to be used and how our equation should be set up. I will also incorporate strategies like pair-share at this time so I can be available/keep a close eye on students that tend to struggle more than others. We will continue this until I have determined all students understand the process and how to decide which function to use based on what information the given right triangle has as well as when we should use an inverse function.

Independent Practice/Closure
To wrap up the lesson, I will revisit and restate the objectives of the day and summarize what we accomplished. I will also use some verbal response tactics to revisit SOH, CAH, TOA. This will look like:
Me: “Sine equals”
Students (in unison hopefully): “opposite over hypotenuse”
I will then ask if there are any remaining questions from the students. Lastly, they will be assigned a formative assessment to work on while I maneuver the room to make sure they are all doing the correct steps.

 Materials: Portable