### Unit 7: Right Triangle Trigonometry

In this unit we, will explore basic trigonometry. We use trigonometry for several types of measuring techniques, such as calculating the height of a building when you know how far away you are standing from a building and the angle of your gaze to the top. Sailors used trigonometry to determine distances and set their course by using the stars as their guide.

**Completing this unit should take you approximately 3 hours.**

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

- explain and apply the Pythagorean theorem;
- calculate the three basic trigonometric functions of a given angle; and
- calculate the sides of a 45-45-90 or 30-60-90 triangle.

### 7.1: The Pythagorean Theorem

The Pythagorean theorem allows us to calculate the lengths of the sides of a triangle. We use it frequently to solve for the unknown length of a side of a triangle.

Watch this introductory video.

Watch this video on how to use the Pythagorean theorem to solve for the length of an unknown side of a triangle.

Then, complete these practice problems and check your answers.

### 7.2: 45-45-90 Triangles

Now that we know the general form of the Pythagorean theorem and how to use it, we can begin exploring special types of triangles and their properties. The first type of triangle we will study is the 45-45-90 right triangle, which is also known as an isosceles triangle.

Read this article and watch the videos to learn about the special properties of isosceles triangles. Pay attention to the examples of finding the length of missing side and solving for unknowns. The article also shows how we can divide squares into two isosceles triangles and then use our knowledge of these triangles to solve for an unknown.

Then, complete review questions 9–12 and check your answers.

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

The other type of right triangle are 30-60-90 right triangles. These triangles have the special property that their side lengths are always related by a specific ratio.

Read this article and watch the videos. Pay attention to the 30-60-90 theorem, which gives the ratio needed to solve for an unknown side of this type of triangle.

Then, complete review questions 5–8 and check your answers.

### 7.4: Sine, Cosine, and Tangent

When performing calculations with triangles, as we have seen, we often are interested in ratios between lengths of the sides of the triangle. The study of trigonometry is the study of these ratios.

Read this page and watch the video. This gives a good overview of the three main trigonometric functions: sine, cosine, and tangent. It may be helpful to write the definitions down for yourself to keep track of them.

Then, take this assessment and check your answers.

### 7.5: Trigonometric Ratios with a Calculator

Finally, we need to learn to use a calculator to solve for sine, cosine, and tangent.

Read this article and watch the videos to learn how to input trigonometric functions into your calculator.

Then, complete review questions 1–3 and check your work to make sure you are able to use your calculator correctly.