Published on 03/30/2007

#### Activity Overview

Using TI Navigator, Cabri Jr and LearnCheck, students will explore how changing the changing an angle in a triangle changes the ratio of the sides, and changing the sides can make changes an angle in a triangle. Students will then explore two different pairs of sides, in the same ratio, will give them the same angle.

#### Before the Activity

Students will define each of the three basic trigonometric ratios, sine, cosine and tangent. Students will be given a do now in learn check using those ratios.

#### During the Activity

Send the students the file tri and tri2.apv Students are to open this file within Cabri Jr. Have the students create another triangle, by dragging various vertices, which has the same angle A as the triangle given, but different lengths of the legs or the hypotenuse. Discuss what happens to cosine A if the angle remains the same, but the legs change. **Make sure that Angle C stays at 90 degrees*** Answer the following questions: - How does the Cos A change? when the angle remains the same? - Is there a relation between the angle and cos A? Screen capture various students? attempts and discuss. Students should then open tri2 within cabri Jr. Using the triangle given, have students drag the vertices to create another triangle that has the same tangent ratio for angle A as , but different lengths of the sides. Screen capture different students attempts, discuss. Answer the following questions: - How does the angle A change as tan A stays the same? - Is there a relation between the angle and tan A? - What relation is there between the sides that give the same tangent ratio?

#### After the Activity

Discuss how to determine the angle given a ratio using the TI-83/84 calculator. Have students practice with various problems.