By now, you're probably familiar with the 3 main ratios used within right-triangle trigonometry. If [b][color=#b20ea8]angle A is an acute angle of any RIGHT TRIANGLE[/color][/b], then you've already learned that: [b][color=#0a971e]sine of A[/color] = [color=#0a971e]leg opposite A[/color] / hypotenuse [color=#c51414]cosine of A[/color] = [color=#c51414]leg adjacent A[/color] / hypotenuse [color=#1551b5]tangent of A[/color] = [color=#0a971e]leg opposite A[/color] / [color=#c51414]leg adjacent A[/color][/b] 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]. Interact with the applet below for a few minutes and then answer the questions that follow.
Key Questions: 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. 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. 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? Other Questions: Determine the measure(s) of an acute angle of a right triangle for which.... 4) The length of the opposite leg is 50% the length of the hypotenuse. 5) The length of the adjacent leg is 50% the length of the hypotenuse. 6) The length of the opposite leg is 50% the length of the adjacent leg. 7) The length of the opposite leg is 80% the length of the hypotenuse. 8) The length of the adjacent leg is 80% the length of the hypotenuse.