# Activity #3__ More on Tangent of an Angle

- Author:
- glassfordpeak, Tim Brzezinski

- Topic:
- Cosine, Ratios, Right Triangles, Sine, Triangles, Trigonometry

## What's Behind the Tangent of an Acute Angle?

For this activity, only slide the . Then see below for instructions.

**TANGENT**slider to conceptually see the meaning of the tangent ratio within this right triangle context. Spend a few minutes interacting with the applet. You can move the 2 LARGER WHITE VERTICES of the triangle anywhere you'd like. The black ACUTE ANGLE slider (or input box below it) is used to change the size of angle**EXPLORATORY QUESTION**S

**1.**What does the triangle look like when the sliders (tangent and acute angle) are set to the far left? Sketch what you see. Explain the relative sizes (hypotenuse, adjacent leg, and opposite leg). Now move the TANGENT slider to the far right. Write down what appears in the upper left corner. Explain the meaning of this.

**2.**Reset the TANGENT slider to the far left. Adjust the acute slider to 15 degrees. Sketch what you see. Now move the TANGENT slider to the far right. Tan (15

**3.**Reset the TANGENT slider to the far left. Adjust the acute angle so that it's bigger than 15 degrees but less than 45 degrees. Sketch what you see. Explain the numerical values and words in the upper left corner. The _________ leg is ____% as long as the _______ leg.

**4.**Reset the TANGENT slider to the far left. Set the acute angle to 45 degrees. Sketch what you see. Move the TANGENT slider to the right and explain what the Tan (45 ) means. The ______ leg is ___% as long as the ____ leg.

**5.**Reset the TANGENT slider to the far left. Set the acute angle to a value between 45 and 89 degrees...say 60 degrees. Sketch what you see. Move the TANGENT slider to the right and explain what the Tan ( ) means. The ______ leg is ___% as long as the ____ leg.

**6.**Reset the TANGENT slider to the far left. Set the acute angle to 90 degrees. Sketch what you see. Move the TANGENT slider to the right and explain what the Tan (90 ) means. The ______ leg is ___% as long as the ____ leg.