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Home › Courses › Pre-Algebra › Archive for Chapter 11: Right Triangles and An Introduction to Trigonometry
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Chapter 11: Right Triangles and An Introduction to Trigonometry

This chapter is nothing short of mathemagical!!! You will begin with a study of square roots of perfect squares (positive and negative roots) and classifying numbers as rational or irrational. From there it will be time to explore the Pythagorean Theorem and seeing how the Theorem leads to The Distance Formula. You will then learn about the Midpoint Formula before spending time with the foundations of similar figures. Similar figures acts as a great connection to special right triangles -> 30-60-90 and 45-45-90 triangles!!! The chapter closes out with a deep dive into trigonometry where sine, cosine, and tangent are learned!! You may have heard of this as SOH-CAH-TOA. Word problems involving angles of elevation and depression cap off an epic chapter of math! Trigonometry sounds scary…but you will see it can be made simple – now go check it all out!!!

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Lesson 1 – Square Roots and Irrational Numbers

Posted on April 22, 2019 by PSM-MattG
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Posted in Chapter 11: Right Triangles and An Introduction to Trigonometry

Lesson 2 – Pythagorean Theorem

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Lesson 3 – Distance and Midpoint Formulas

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Lesson 4 – Similar Figures

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Lesson 5 – Special Right Triangles

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Lesson 6 – Introduction to Trigonometry

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Lesson 7 – Trigonometry Word Problems and Angles of Elevation & Depression

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    January 16, 2017
  • My son Griffin took Matt's AP Clac summer class he thoroughly enjoyed Matt's style of teaching and felt the class will prepare him for AP Calc this year. I highly recommend Matt and any of his classes!

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    January 15, 2017
  • Mr. Groden really helped me learn the subject of geometry very well. He related certain topics to the interest of the student which helped a lot. The pointers he gave for study habits were definitely very helpful and I would recommend Mr. Groden to anybody.

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    June 8, 2018

    Matt is incredible at translating the difficult to understand into easy to learn concepts. He helped our son who was struggling with calculus to attain good grades. We can't recommend him highly enough !

    Dena Cimakosky Scalamandre Avatar Dena Cimakosky Scalamandre
    January 22, 2017
  • My son had Mr. Groden as a teacher at PHS and my daughter attending Summer AP Calc Prep. Matt does the unthinkable, he makes Calc fun for his students and they are not afraid to make mistakes or ask for help. My daughter feels more confident having attended "math camp". Thank you!

    Tamie Palatine Avatar Tamie Palatine
    August 13, 2017

    positive review  I can't say enough good things about Mr. Groden! He has helped my son so much. My son fights working with tutors but Mr. Groden did an excellent job pairing with my son and making him feel comfortable with him. He really understands the areas that my son struggles with and helps him in those areas while at the same time giving my son positive feedback and encouraging him. It gives me peace of mind knowing that with Mr. Groden's help my son will do well and grow and learn and be successful in his math classes!

    Amy Cimino Bodnar Avatar Amy Cimino Bodnar
    January 25, 2019
  • I think it is clear to anyone who has worked with Mr. Groden that he has a very special ability to empower and inspire the youth, and to teach in ways that resonate for all. His patience, compassion, flexibility, and incredibly thorough understanding of the math combine to help students realize our greatest potential -- sometimes potential that we didn’t even know was there until he helped us find it. In addition to being an amazing teacher, he is a great role model and friend to anyone he meets. So easy to talk to, so caring, so kind -- the most genuine person. I would be doing a disservice to the community if I did not spread the world about the incredible opportunity to learn with him. 5million stars

    Avery Willner Avatar Avery Willner
    January 19, 2018

    positive review  Love. :) My daughter took Matt’s AP Calc prep class, and my son watched the algebra prep videos. Both loved, especially my daughter who now wants to sign up for every class Matt offers. Thank you for approaching teaching in such a fun and engaging way!! So highly recommend. :)

    Erica Desrosiers Avatar Erica Desrosiers
    August 16, 2019
  • positive review  Mr. Groden is an energetic, dynamic teacher who truly cares about his students. He uses real-world examples and innovative teaching practices to help his students learn the concepts and to develop a passion about mathematics.

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    August 17, 2018

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    Tina Mohsen Avatar Tina Mohsen
    February 7, 2017
  • Because he was in this class, my son spent more time doing SAT practice tests this summer than he otherwise would have. I didn't have to "nag" him to do practice tests...so, I appreciate that! He ended up knowing alot of the kids in the class, so he enjoyed it. It was also nice to do this in the summer when his schedule was less-busy. The teachers are high energy, well-respected and admired by the kids.

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    September 7, 2017

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    October 11, 2017
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      • 6th Grade Math
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Whole Numbers & Decimals
        • Chapter 2: Representing Data In Different Ways
        • Chapter 3: Variables, Algebraic Expressions, & Solving Equations
        • Chapter 4: Divisibility, Factoring Numbers, & Fractions
        • Chapter 5: Addition and Subtraction of Fractions
        • Chapter 6: Multiplication and Division of Fractions
        • Chapter 7: Ratios, Proportions, and Percents
        • Chapter 8: Fundamentals of Geometry
        • Chapter 9: Unit Conversions, Perimeter, Area, & Volume
        • Chapter 10: Introduction to Probability
        • Chapter 11: Integers – Properties, Operations, & Equations
        • Chapter 12: Two-Step Equations and Inequalities
      • Pre-Algebra
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions & Operations with Integers
        • Chapter 2: One-Step Equations & Inequalities
        • Chapter 3: Operations and Equations With Decimals
        • Chapter 4: Factors, Simplifying Fractions, and Exponent Rules
        • Chapter 5: Fraction Operations & Solving Equations with Fractions
        • Chapter 6: Operations and Uses of Ratios, Proportions, & Percents
        • Chapter 7: Solving Equations and Inequalities
        • Chapter 8: Relations & Functions, Slope, Lines, and Graphing
        • Chapter 9: Foundations of Geometry
        • Chapter 10: Areas of Two- & Three-Dimensional Figures and Volume
        • Chapter 11: Right Triangles and An Introduction to Trigonometry
        • Chapter 12: Data Analysis: Techniques and Calculations
        • Chapter 13: Probability, Combinations, and Permutations
        • Chapter 14: Foundations of Non-Linear Functions and Polynomial Operations
      • Algebra 1
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1: Algebraic Expressions and Operations with Real Numbers
        • Chapter 2: Solving Equations – From One-Step to Multi-Step
        • Chapter 3: Ratios, Proportions, & Percents
        • Chapter 4: Solving Inequalities
        • Chapter 5: Introduction to Graphs and Functions
        • Chapter 6: Linear Functions and Graphing Lines
        • Chapter 7: Systems of Linear Equations and Linear Inequalities
        • Chapter 8: Exponent Rules & Exponential Functions
        • Chapter 9: Polynomials
        • Chapter 10: Graphing and Solving Quadratic Equations
        • Chapter 11: Introduction to Rational Expressions
        • Chapter 12: Radicals and An Introduction to Trigonometry
        • Chapter 13: Data Analysis: Techniques and Calculations
        • Chapter 14: Probability, Combinations, and Permutations
      • Calculus 1 & 2 / AB / BC
        ▼
        • Course Overview
        • How to Maximize Your Learning Experience!
        • Chapter 1 – Limits
        • Chapter 2 – Derivatives
        • Chapter 3 – Uses of the Derivative
        • Chapter 4 – Integration
        • Chapter 5 – Derivatives and Integrals of Exponential Functions, Logarithms, and Inverse Trigonometry
        • Chapter 6 – Differential Equations and Exponential & Logistic Growth
        • Chapter 7 – Area, Volume, and Arc Length
        • Chapter 8 – Advanced Integration Techniques and Improper Integrals
        • Chapter 9 – Series and Tests for Convergence and Divergence
        • Chapter 10 – Taylor Polynomials and Power Series
        • Chapter 11 – The Calculus of Parametric and Polar Equations
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