# Chapter 8: Right Triangle Trigonometry

**Basic**Created by: CK-12

## Introduction

This chapter takes a look at right triangles. A right triangle is a triangle with exactly one right angle. In this chapter, we will prove the Pythagorean Theorem and its converse. Then, we will discuss trigonometry ratios and inverse ratios.

- 8.1.
## Expressions with Radicals

- 8.2.
## Pythagorean Theorem and Pythagorean Triples

- 8.3.
## Applications of the Pythagorean Theorem

- 8.4.
## Inscribed Similar Triangles

- 8.5.
## 45-45-90 Right Triangles

- 8.6.
## 30-60-90 Right Triangles

- 8.7.
## Sine, Cosine, Tangent

- 8.8.
## Trigonometric Ratios with a Calculator

- 8.9.
## Trigonometry Word Problems

- 8.10.
## Inverse Trigonometric Ratios

### Chapter Summary

## Summary

This chapter begins with a review of how to simplify radicals, an important prerequisite technique for working with the Pythagorean Theorem. The Pythagorean Theorem, its converse, and Pythagorean triples are discussed in detail. Applications of the Pythagorean Theorem are explored including finding missing lengths in right triangles. The chapter then branches out into applications of special right triangles, namely 45-45-90 and 30-60-90. The connection between trigonometry and geometry is explored through trigonometric ratios, trigonometry word problems and inverse trigonometric ratios at the end of this chapter.

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