# Ch 3: Common Core HS Geometry: Trigonometry

### About This Chapter

**Standard:** Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. (CCSS.Math.Content.HSG-SRT.C.6)

**Standard:** Explain and use the relationship between the sine and cosine of complementary angles. (CCSS.Math.Content.HSG-SRT.C.7)

**Standard:** Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. (CCSS.Math.Content.HSG-SRT.C.8)

**Standard:** Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. (CCSS.Math.Content.HSG-SRT.D.9)

**Standard:** Prove the Laws of Sines and Cosines and use them to solve problems. (CCSS.Math.Content.HSG-SRT.D.10)

**Standard:** Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). (CCSS.Math.Content.HSG-SRT.D.11)

## About This Chapter

An understanding of the principles of trigonometry allows students to define trigonometric ratios and solve problems involving right triangles. They will be able to apply trigonometry to general triangles and prove the Laws of Sine and Cosine and use them to solve problems.

The lessons in this standard include the following topics:

- Sine and cosine
- Trigonometric ratios and similarity
- Application of the Pythagorean Theorem
- Solving right triangles
- Finding area
- Laws of Sine and Cosines and how to apply them

Students can show they've mastered this standard by determining the area of triangles and using the Laws of Sine and Cosine to find measurements in right and non-right triangles. This standard and these lessons can ready students for higher education and possibly careers in such fields as surveying, engineering, architecture and mathematics.

### How to Use These Lessons in Your Classroom

Here are some methods you can use to incorporate our lessons on trigonometry into your curriculum to help meet the common core standards:

#### Solving Right Triangles

Watch the lesson on *Solving Right Triangles* as a class or as a homework assignment, then work together on the practice problems in the following lesson.

#### Pre-Quiz and Post-Quiz Lessons

Have students take the quiz for the *Sine and Cosine* lesson, then go over the answers as a class and watch the lesson together. Go back and retake the quiz to assess their learning.

#### The Pythagorean Theorem

Assign the lessons on The Pythagorean Theorem as homework or for in-class viewing. Divide the class into small groups and ask them to come up with two or three word problems that require utilizing the Pythagorean Theorem to solve. Combine the questions into one quiz and give it to the whole class. Review the answers together.

### 1. Trigonometry: Sine and Cosine

Learn an easy trick to help you solve trigonometry problems, including problems with sine, cosine and inverse trig functions. At the end of this lesson, you'll know what SohCahToa means and how to use it.

### 2. 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.

### 3. 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.

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### Other Chapters

Other chapters within the Common Core Math - Geometry: High School Standards course