1. Introduction to Trigonometry Unit IIC Day 3

2. Do Now Are the following triangles similar? If so, how would you prove it?

3. Trigonometry Trigonometry is the study of ratios of sides in right triangles. We refer to sides in relation to a given angle as opposite the angle, adjacent to the angle, or as the hypotenuse.

4. Ex. 1: Identifying Side Lengths a) If you are “standing” at vertex D, which side is the hypotenuse? Which is the opposite side? Which is the adjacent side? b) If you are “standing” at vertex E, which side is the hypotenuse? Which is the opposite side? Which is the adjacent side?

5. Note on Sides We never “stand” at the right angle. The hypotenuse is the hypotenuse; it is never considered adjacent even though it might appear to be.

6. Ex. 2: Ratios “Standing” at vertex G, what is the ratio of the opposite side to the adjacent side? What does this ratio represent?

7. Ex. 2A: Ratios “Standing” at vertex B, what is the ratio of the opposite side to the adjacent side? What does this ratio represent?

8. Ex. 3: Comparing Ratios a) Standing at angle A, what is the ratio of the opposite side to the adjacent side? b) Standing at angle D, what is the ratio of the opposite side to the adjacent side? c) Standing at angle G, what is the ratio of the opposite side to the adjacent side? What can we conclude about the ratio of the opposite to the adjacent anytime we are standing at the 45  angle of any right triangle?

9. The Tangent Function The tangent of an angle in a right triangle is the ratio of the opposite side length to the adjacent side length. We can think of tangent as a function that takes an angle measure as its input and gives the ratio opposite/adjacent as its output. Angle (º)15º30º45º60º Opp./Adj.

10. Ex. 4: Finding Tangent a) Find the tangent of  R. a) Find the tangent of  S.

11. Ex. 5: Comparing Tangents Find the tangent of  A for both triangles. Compare your results.