## Solving Right Triangles Using Trigonometry

### Johnny WolfeSanta Rosa District Schools

#### Description

This lesson covers solving techniques using trigonometric ratios for right triangles.

#### 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 Solving Right Triangles Using Trigonometry (see attached file)
-Solving Right Triangles Using Trigonometry Examples (see attached file)
-Solving Right Triangles Using Trigonometry Activity Sheet (see attached file)
-Solving Right Triangles Using Trigonometry Checklist (see attached file)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Solving Right Triangles Using Trigonometry Examples. (See attached file.)

2. Have marking pens (for overhead).

3. Make copies of Solving Right Triangles Using Trigonometry Examples for students. (See attached file.) Be prepared and ready to demonstrate to students.

4. Have enough copies of Solving Right Triangles Using Trigonometry Activity Sheet for each student. (See attached file.)

5. Have enough copies of Solving Right Triangles Using Trigonometry Checklist for each student. (See attached file.)

#### 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, exponents,absolute value, and logarithms. This lesson does not address exponents. This lesson does not address ratio and proportion.

1. Discuss with students what it means to solve a triangle and that they must use their problem-solving ability to determine which ratio to use. (See # 1 on attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

2. Review with students the trigonometric ratios. (See # 2 on attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

3. Discuss Thought Provoker with students. (See # 3 on attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

4. Work example 4. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

5. Discussing with students alternative methods for checking results. (See
# 5 on attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

6. Ask students how they would use the cosine ratio to solve for angle A in example 4. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

7. Ask students how they would use the tangent ratio to solve for angle A in example 4. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

8. Work example # 8. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

9. Work example # 9. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

10. Have students use sin 50 = x/7.6 to solve for the measure of line segment DE in example 9. (See attached file: Solving Right Triangles Using Trigonometric Examples.) Answer students' questions and comments.

11. Work example # 11. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

12. Ask students to explain why the tangent ratio is used in example 11. (See # 12 on attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

13. Work example # 13. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

14. Work example # 14. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

15. Work example # 15. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

16. Work example # 16. (See attached file: Solving Right Triangles Using Trigonometry Examples.) Answer students' questions and comments.

17. Distribute the Solving Right Triangles Using Trigonometry Activity Sheet. (See attached file.)

18. Distribute the Solving Right Triangles Using Trigonometry Checklist. (See attached file.) Discuss assessment criteria.

19. The students will write their responses on the activity sheet.

20. The teacher will move from student to student observing the students' work and lending assistance.

21. Assess activity sheet responses.

#### Assessments

Students' activity sheets will be taken up and scored according to Solving Right Triangles Using Trigonometry Checklist. (See attached file.)

#### Extensions

Cut out several triangles on card stock. Have students carefully measure the acute angles and record their results. Next, have students use the following equation by substituting their angle values into A and B: Sin
2 (A) + Cos
2 (B) = N (read as sine squared of angle A plus the cosine squared of angle B). Allow students to discuss what they discovered about the value N.