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?