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

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.

Follow the Activity procedures:

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