# Ch 3: Common Core HS Geometry: Trigonometry

Students can use these lessons on trigonometry to prepare to meet common core high school geometry standards. Find out how to incorporate these lessons into your classroom teaching.

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)

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.

3 Lessons in Chapter 3: Common Core HS Geometry: Trigonometry
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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