# Exploring Trigonometric Ratios

## G-SRT.3.6

In this activity, students will

**relate the definitions of trigonometric ratios to a property of similar triangles.**## Triangle ADE

Note that dragging

*E*moves Line*DE*along Ray*AB*. Line*DE*was constructed to be perpendicular to Ray*AB*. This makes Triangle*ADE*a right triangle.As you drag *E*, Triangle *ADE* is changed, but what relationship exists between all these versions of Triangle *ADE*?

## Note that dragging C changes the measure of Angle A.

As you drag *C*, Triangle *ADE* is changed, but what relationship exists between all these versions of Triangle *ADE*?

## Exploring Trigonometric Ratios Worksheet (don't worry about this if you've received the worksheet in class)

## Use this to complete the tables 1 and 3 on the Exploring Trigonometric Ratios Worksheet

## Answer this question after you've completed Table 1.

When you compared the values in Table 1 to values in a trigonometric table, what column did they match with?

## Table 1

What did you observe about the multiple trials using the same angle in Table 1?

## Answer this question after you've completed Table 3.

When you compared the values in Table 3 to values in a trigonometric table, what column did they match with?

## Table 3

What did you observe about the multiple trials using the same angle in Table 3?

## VOCABULARY

Remember that

**complementary angles**add up to 90 degrees.## Compare the values in table 1 to the values of the complementary angles in table 2.

What do you notice?