### Unit 7: Right Triangle Trigonometry

In this unit, you will learn the basics of trigonometry. Trigonometry is used for several different measuring techniques. You can determine the height of a building, for example, if you know how far away you are standing and at what angle your eyes form when looking up to its top. In previous centuries, mariners could use trigonometry to help them set their course, using the heavens as a guide.

**Completing this unit should take you approximately 11 hours.**

Upon successful completion of this unit, you will be able to:

- explain and apply the Pythagorean Theorem;
- find the three basic trig functions of a given angle; and
- find the sides of a 45-45-90 or 30-60-90 triangle.

### 7.1: Pythagorean Theorem

Take notes as you watch this video to understand the Pythagorean Theorem. Watch this presentation carefully two or three times to understand how to find missing sides by using this formula.

Read this section, which provides examples of applying the Pythagorean Theorem. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the Pythagorean Theorem.

Read this section, which discusses how to identify triangle types from the Pythagorean Theorem. Then, complete the practice problems. These questions will provide you with the opportunity to determine triangles by using the Pythagorean Theorem.

### 7.2: 45-45-90 Triangles

Take notes as you watch this video to understand the relationship between the angles and sides of a 45-45-90 triangle. Watch this presentation carefully two or three times to understand how to find missing sides using this triangle.

Read this section, which discusses 45-45-90 right triangles. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the relationship between the sides of a 45-45-90 right triangle.

### 7.3: 30-60-90 Right Triangles

Take notes as you watch this video to understand the relationship between the angles and sides of a 30-60-90 triangle. Watch this presentation carefully two or three times to understand how to find missing sides by applying the properties of this triangle.

Read this section, which discusses 30-60-90 right triangles. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the relationship between the sides of a 30-60-90 right triangle.

Complete this assessment, which tests your knowledge on finding the missing sides of special right triangles. You can review the concepts associated with these questions with the Khan videos from subunits 7.2 and 7.3.

### 7.4: Sine, Cosine, and Tangent

Read this section, which discusses trigonometric ratios. Then, complete the practice problems. These exercises will provide you with the opportunity to apply the relationships of various trigonometric ratios.

Complete this assessment, which tests your knowledge on basic trigonometric ratios. You can review the concepts associated with these questions from subunit 7.4.

### 7.5: Trigonometric Ratios with a Calculator

Read this section, which discusses finding trigonometric ratios with a calculator. Then, complete the practice problems. These exercises will provide you with the opportunity to use a calculator to find various trigonometric ratios.