For this activity, only slide the [b]TANGENT [/b]slider to conceptually see the meaning of the tangent ratio within this right triangle context.[br][br]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 [math]\alpha[/math] . Then see below for instructions.

[b]EXPLORATORY QUESTION[/b]S[br][br][color=#0000ff][b]1. [/b][/color][br]What does the triangle look like when the sliders (tangent and acute angle) are set to the far left? [br]Sketch what you see. [br]Explain the relative sizes (hypotenuse, adjacent leg, and opposite leg).[br]Now move the TANGENT slider to the far right. [br]Write down what appears in the upper left corner. Explain the meaning of this.[br][br][color=#38761d][b]2.[/b][/color][br]Reset the TANGENT slider to the far left.[br]Adjust the acute slider to 15 degrees.[br]Sketch what you see.[br]Now move the TANGENT slider to the far right.[br]Tan (15[math]^\circ[/math] ) is approximately equal to what value?[br]Explain what the value means in terms relative sizes of the legs.[br]The _________ leg is ____% as long as the _______ leg.[br][br][color=#ff0000][b]3.[/b][/color][br]Reset the TANGENT slider to the far left.[br]Adjust the acute angle so that it's bigger than 15 degrees but less than 45 degrees.[br]Sketch what you see.[br]Explain the numerical values and words in the upper left corner.[br]The _________ leg is ____% as long as the _______ leg.[br][color=#ff7700][b]4.[/b][/color][br]Reset the TANGENT slider to the far left.[br]Set the acute angle to 45 degrees.[br]Sketch what you see.[br]Move the TANGENT slider to the right and explain what the Tan (45 ) means.[br]The ______ leg is ___% as long as the ____ leg.[br][br][b][color=#ffff00]5. [/color][/b][br]Reset the TANGENT slider to the far left.[br]Set the acute angle to a value between 45 and 89 degrees...say 60 degrees.[br]Sketch what you see.[br]Move the TANGENT slider to the right and explain what the Tan ( ) means.[br]The ______ leg is ___% as long as the ____ leg.[br][br][color=#783f04][b]6. [/b][/color][br]Reset the TANGENT slider to the far left.[br]Set the acute angle to 90 degrees.[br]Sketch what you see.[br]Move the TANGENT slider to the right and explain what the Tan (90 ) means.[br]The ______ leg is ___% as long as the ____ leg.