Unit 7 test study guide right triangles and trigonometry answer key

Right Triangles and Trigonometry (Geometry Curriculum - Unit 7) | All Things Algebra®

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Unit 7: Right Triangle Trigonometry
7.1: The Pythagorean Theorem
7.2: 45-45-90 Triangles
7.3: 30-60-90 Right Triangles
7.4: Sine, Cosine, and Tangent
7.5: Trigonometric Ratios with a Calculator

DISTANCE LEARNING UPDATE: This unit now contains a Google document with:

(1) Links to instructional videos. Videos are created by fellow teachers for their students using the guided notes from the unit. Please watch through first before sharing with your students. They might not always be perfect but we are trying our best to help out where we can in a very limited time.

(2) A link to a Google Slides version of the unit. Each page is set to the background in Google Slides. There are no text boxes; this is the PDF in Google Slides. We are unable to do text boxes at this time but hope this saves you a step if you wish to use it in Slides instead!

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This bundle contains notes, homework assignments, three quizzes, a study guide and a unit test that cover the following topics:

• Pythagorean Theorem and Applications

• Pythagorean Theorem Converse and Classifying Triangles

• Special Right Triangles: 45-45-90 and 30-60-90

• Similar Right Triangles

• Geometric Mean

• Trigonometric Ratios: Sine, Cosine, and Tangent

• Finding Missing Sides using Trigonometry

• Finding Missing Angles using Trigonometry

• Trigonometry Applications: Angle of Elevation and Angle of Depression

• Law of Sines

• Law of Cosines

• Solving Triangles

• Law of Sines and Law of Cosines Applications

NEW: Assessments are now EDITABLE! Now you can easily make multiple versions or customize to fit your needs! PowerPoint and Equation Editor (usually built in to PowerPoint) are required to edit these files. There is a folder titled "Editable Assessments" when you download. This is where you will find editable versions of each quiz and the unit test. If your Equation Editor is incompatible with mine, simply delete my equation and insert your own.

This resource is included in the following bundle(s):

Geometry Second Semester Notes Bundle

Geometry Curriculum

Geometry Curriculum (with Activities)

More Geometry Units:

Unit 1 – Geometry Basics

Unit 2 – Logic and Proof

Unit 3 – Parallel and Perpendicular Lines

Unit 4 – Congruent Triangles

Unit 5 – Relationships in Triangles

Unit 6 – Similar Triangles

Unit 8 – Polygons and Quadrilaterals

Unit 9 – Transformations

Unit 10 – Circles

Unit 11 – Volume and Surface Area
Unit 12 – Probability

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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.