## 30-60-90 Right Triangles and Algebra

### Johnny WolfeSanta Rosa District Schools

#### Description

This lesson covers right triangle relationships of the 30-60-90 triangle.

#### Objectives

Understands that numbers can be represented in a variety of equivalent forms using integers, fractions, decimals, and percents, scientific notation, exponents, radicals, absolute value, or logarithms.

Understands and explains the effects of addition, subtraction, multiplication and division on real numbers, including square roots, exponents, and appropriate inverse relationships.

Adds, subtracts, multiplies, and divides real numbers, including square roots and exponents using appropriate methods of computing (mental mathematics, paper-and-pencil, calculator).

represents and applies geometric properties and relationships to solve real-world and mathematical problems including ratio, proportion, and properties of right triangle trigonometry.

#### Materials

-Overhead transparencies (if examples are to be worked on overhead) for 30-60-90 Right Triangles and Algebra (See Associated File)
-30-60-90 Right Triangles and Algebra Examples (See Associated File)
-30-60-90 Right Triangles and Algebra Worksheet (See Associated File)
-30-60-90 Right Triangles and Algebra Checklist (See Associated File)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for 30-60-90 Right Triangles and Algebra Examples. (See Associated File)
2. Have marking pens (for overhead).
3. Have 30-60-90 Right Triangles and Algebra Examples (See Associated File) prepared and ready to demonstrate to students.
4. Have enough copies of 30-60-90 Right Triangles and Algebra Worksheet (See Associated File) for each student.
5. Have enough copies of 30-60-90 Right Triangles and Algebra Checklist (See Associated File) for each student.

#### Procedures

Prior Knowledge: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals and solving equations.
Note: This lesson does not address percents, scientific notation, absolute value, and logarithms. This lesson does not address ratio and proportion.

1. Review with students on naming angles and sides of a triangle. (See #1 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

2. Describe to students why we call these 30-60-90 triangles. Make sure students understand what an acute angle is. (See #2 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

3. Ask students to analyze the equilateral triangle and to come up with the measure of angle B. Make sure students know what constitutes an equilateral triangle. (See #3 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

4. Ask students to draw a perpendicular to the base of triangle ABC. Then have students determine what type of triangles are formed. Make sure students understand what a perpendicular line segment is. (See #4 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

5. Discuss Thought Provoker. Make sure students understand the term bisect. (See #5 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

6. Discuss the measure of the side opposite the 30-degree angle. (See #6 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

7. Discuss how we label triangles. (See #7 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

8. Work #8 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

9. Work #9 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

10. Work #10 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

11. Work #11 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

12. Work #12 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

13. Have students do the Thought Provoker. (See #13 on 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

14. Work #14 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

15. Work #15 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

16. Work #16 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

17. Work #17 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

18. Work #18 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

19. Work #19 example. (See 30-60-90 Right Triangles and Algebra Examples) Answer student questions and comments.

20. Distribute the 30-60-90 Right Triangles and Algebra Worksheet. (See Associated File)

21. Distribute the 30-60-90 Right Triangles and Algebra Checklist. (See Associated File) Describe what constitutes an A, B, C, D, and F in the Checklist.

22. The students write their responses on the worksheet.

23. The teacher moves from student to student observing their work and lending assistance.

#### Assessments

Student worksheets are taken up and scored according to 30-60-90 Right Triangles and Algebra Worksheet Key and Checklist. (See Associated File) These scores may be placed in the grade book.

#### Extensions

Have students take a protractor and measure objects that have 30-60-90 degree angles. Then, using the concepts learned when using a 30-60-90 triangle, determine the length of the diagonal. Then have students measure the diagonal and compare with their computations.