# Activities

• • • ##### Subject Area

• Math: Precalculus: Trigonometry (Triangle and Circular Functions)

• ##### Author 9-12

45 Minutes

• ##### Device
• TI-73 Explorer™
• TI-Navigator™
• ##### Other Materials
ruler, protractor

## Trigonometry ratios: Tangent Ratio

#### Activity Overview

In this activity, students will look at the tangent ratio and use triangle constructions to explore the concepts of trigonometric ratios. The tangent ratio specifically will then be practiced.

#### Before the Activity

Students should be able to identify the sides of a right triangle in relation to a specific angle (i.e., opposite, adjacent and hypotenuse). They should also be able to construct a right triangle using a ruler and protractor. Students should be familiar with how to: log in to the TI-Navigator system and access LearningCheck documents.

#### During the Activity

The instructor should first review how to identify the opposite, adjacent and hypotenuse in a right triangle, reminding students that these sides relate to a specific angle.
Next, the instructor should explain the tangent ratio. Have each student use a ruler and protractor to construct a right triangle (30?, 60?, 90?). The length of sides do not matter, however the angles do. Now have students measure the length of each side and record it. Next have students find the ratio of O/A for the 30? angle. Ask students to submit their ratio using Quick Poll. The ratios should be close despite many different lengths of sides and thus we discuss what tangent refers to. Students should then be shown how to use the calculator to find the tangent of an angle, as well as how to find the angle given its tangent. Have students practice these skills by completing the LearnCheck document attached below.

Students should work through the questions and then the teacher should collect the file from the students. Use the slide show component of Class Analysis to share and discuss answers to the LearnCheck Practice Questions.

#### After the Activity

Retention of knowledge should be checked during the following classes. Quick Poll could be used very effectively to check this information. A similar process could be used with sine or cosine functions as well.