# Activities

• • • ##### Subject Area

• Math: Geometry: Triangles

• ##### Author 9-12

60 Minutes

• ##### Device
• TI-83 Plus Family
• TI-84 Plus
• TI-84 Plus Silver Edition
• ##### Software

Cabri Geometry™
TI Connect™

• ##### Accessories

TI Connectivity Cable

• ##### Other Materials
This is Activity 14 from the EXPLORATIONS Book:
Exploring The Basics Of Geometry With Cabri

## Sin, Cos, and Tan of Right Triangles

#### Activity Overview

In this activity, students explore a right angled triangle and its trigonometric concepts. They investigate the trigonometric ratios for the angles of the triangle.

#### Before the Activity

Install the Cabri™: Jr. App on the students' graphing calculators using one of these two methods:

• TI-Connect™,  a TI Connectivity Cable, and the Unit-to-Unit Link Cable
• TI-Navigator™  "send to class" feature
• See the attached PDF file for detailed instructions for this activity
• Print pages 57 - 60 from the attached PDF file for your class
• #### During the Activity

Distribute the pages to the class.

• Construct a right triangle
• Measure the side lengths and all interior angles of the triangle
• Calculate the ratio of the opposite side to the hypotenuse for the acute angles of the triangle
• Calculate the ratio of the adjacent side to the hypotenuse for the acute angles of the triangle
• Calculate the ratio of the opposite side to the adjacent side for the acute angles of the triangle
• Calculate the sin, cos, and tan values for the acute angles
• Observe that the sin of an angle is the ratio of the opposite side to the hypotenuse, the cos of an angle is the ratio of the adjacent side to the hypotenuse, and the tan of an angle is the ratio of the opposite side to the adjacent side
• Alter the triangle and verify if the relationships hold true
• Note that the sin of one angle equals the cos of the other angle
• Increase the measure of one of the acute angles
• Notice that as the angle gets larger, its sin and tan get larger, whereas cos gets smaller
• #### After the Activity

Review student results:

• As a class, discuss questions that appeared to be more challenging
• Re-teach concepts as necessary