# Ch 41: The Pythagorean Theorem & Trigonometry

### About This Chapter

## The Pythagorean Theorem & Trigonometry - Chapter Summary

Review the lessons in this chapter to develop a more concrete understanding of the Pythagorean theorem and trigonometry. Throughout the chapter, our instructors will explain the most essential information about this topic. These lessons include topics such as:

- Uses of the Pythagorean theorem
- Special cases of the Pythagorean theorem
- Finding triangle side lengths using the theorem
- Functional problems involving Pythagoras' theorem
- Sines, cosines and tangents
- Trigonometric ratios and similarity

The lessons in this chapter will prepare you to solve problems using the Pythagorean theorem and trigonometry. Each lesson comes with a full written transcript. Test what you've learned with our interactive quizzes, and if you have any questions, contact our expert instructors.

### 1. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

### 2. The Pythagorean Theorem: Converse and Special Cases

The Pythagorean Theorem is a famous theorem for right triangles. Watch this video to learn how the Pythagorean Theorem relates to the law of cosines and how the converse of the Pythagorean Theorem can help you identify right triangles.

### 3. How to Find the Hypotenuse of a Right Triangle Using the Pythagorean Theorem

After watching this video lesson, you will be able to use the Pythagorean Theorem and its resultant formula to help you find the length of the hypotenuse of a right triangle when you know the measurements of the triangle's two other sides.

### 4. How to Find Shorter Sides on a Right Triangle Using the Pythagorean Theorem

Sure, the Pythagorean Theorem is useful for finding the hypotenuse of a right triangle, but what about the other sides? As this lesson shows, it's just a matter of flipping the formula.

### 5. How to Solve Functional Problems Involving the Pythagorean Theorem

One of the most useful aspects of studying triangles is the Pythagorean Theorem. In this lesson, we use it to find the unknown length of a side of a triangle, whether it is a shorter side or the hypotenuse.

### 6. Trigonometry and the Pythagorean Theorem

Explore how the Pythagorean Theorem can be used in conjunction with trigonometric functions. In this lesson, take an inverse trigonometric function, and define all three sides of a right triangle.

### 7. Trigonometric Ratios and Similarity

Where do terms like sine, cosine and tangent come from? In this lesson, we'll learn about how similarity with right triangles leads to trigonometric ratios.

### 8. Practice Finding the Trigonometric Ratios

So you know what sine, cosine and tangent are. Great! But how do you use them? Find out how in this lesson as we find missing sides and angles using trigonometric ratios.

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### Other Chapters

Other chapters within the MTLE Middle Level Mathematics: Practice & Study Guide course

- 6th-8th Grade Math: Basic Arithmetic Operations
- 6th-8th Grade Math: Properties of Numbers
- Number Theory & Factoring
- 6th-8th Grade Math: Estimating & Rounding
- 6th-8th Grade Math: Whole Numbers
- 5th Grade Math: Simplifying Whole Number Expressions
- Negative Numbers
- 6th-8th Grade Math: Absolute Value
- 6th-8th Grade Math: Integers
- 6th-8th Grade Math: Rational Numbers
- 6th-8th Grade Math: Inequalities
- 6th-8th Grade Math: Introduction to Fractions
- 6th-8th Grade Math: Operations with Fractions
- 6th-8th Grade Math: Introduction to Decimals
- 6th-8th Grade Math: Operations with Decimals
- 6th-8th Grade Math: Percents
- Working with Rates, Ratios & Proportions
- Practical Applications of Rates, Ratios & Proportions
- Introduction to Exponents
- Working with Exponential Expressions
- Understanding Square Roots & Radical Expressions
- Radical Expressions & Equations
- Imaginary & Complex Numbers
- 6th-8th Grade Algebra: Writing Algebraic Expressions
- Basic Algebraic Expressions & Factoring
- Algebraic Distribution
- 6th-8th Grade Algebra: Writing & Solving One-Step Equations
- 6th-8th Grade Algebra: Writing & Solving Two-Step Equations
- 6th-8th Grade Algebra: Simplifying & Solving Rational Expressions
- 6th-8th Grade Algebra: Linear Equations
- 6th-8th Grade Algebra: Systems of Linear Equations
- 6th-8th Grade Algebra: Monomials & Polynomials
- 6th-8th Grade Math: Properties of Functions
- 6th-8th Grade Math: Graphing Functions
- Rate of Change Basics
- Notation, Sequences & Series
- 6th-8th Grade Measurement: Units of Measurement
- Fundamentals of Geometric Figures & Angles
- Two-Dimensional Shapes
- Circle Geometry
- 6th-8th Grade Measurement: Perimeter & Area
- 6th-8th Grade Geometry: Polyhedrons & Geometric Solids
- Congruence & Similarity in Geometry
- 6th-8th Grade Math: The Coordinate Graph
- 6th-8th Grade Geometry: Transformations
- Modeling to Solve Problems
- Basic Probability
- Statistics & Sampling Basics
- MTLE Middle Level Mathematics Flashcards