By now, you're probably familiar with the 3 main ratios used within right-triangle trigonometry. [br][br]If [b][color=#b20ea8]angle A is an acute angle of any RIGHT TRIANGLE[/color][/b], then you've already learned that:[br][br][b][color=#0a971e]sine of A[/color] = [color=#0a971e]leg opposite A[/color] / hypotenuse[br][color=#c51414]cosine of A[/color] = [color=#c51414]leg adjacent A[/color] / hypotenuse[br][color=#1551b5]tangent of A[/color] = [color=#0a971e]leg opposite A[/color] / [color=#c51414]leg adjacent A[/color][/b][br][br]The applet below depicts the [b]TRUE MEANINGS of the 3 main trigonometric ratios[/b] when used in the context of a [b]right triangle[/b]. [br]Interact with the applet below for a few minutes and then answer the questions that follow.

Key Questions: [br][br]1) Is it ever possible for the length of the opposite leg to ever equal OR exceed 100% of the length of the hypotenuse? Explain why or why not. [br]2) Is it ever possible for the length of the adjacent leg to ever equal OR exceed 100% of the length of the hypotenuse? Explain why or why not. [br]3) Is it ever possible for the length of the opposite leg to equal the length of the adjacent leg? If so, at what acute angle measure(s) does this occur? [br][br]Other Questions:[br][br]Determine the measure(s) of an acute angle of a right triangle for which.... [br][br]4) The length of the opposite leg is 50% the length of the hypotenuse.[br]5) The length of the adjacent leg is 50% the length of the hypotenuse.[br]6) The length of the opposite leg is 50% the length of the adjacent leg.[br]7) The length of the opposite leg is 80% the length of the hypotenuse.[br]8) The length of the adjacent leg is 80% the length of the hypotenuse.