Carefully observe the diagram below. Notice [math]\alpha\ge\beta[/math]. [br][br]Slide the black slider slowly and [b]CAREFULLY OBSERVE THE DYNAMICS THAT TAKE PLACE.[/b] [br][br]After doing so, answer the questions and complete the activity prompts that appear below this applet.
What can we conclude about [math]\bigtriangleup BDC[/math]and [math]\bigtriangleup BAF[/math]? Why can we conclude this?
Given your response to (1), write an equation that expresses the relationship among the lengths [i]AF[/i], [i]AB[/i], [i]CD[/i], and [i]DB[/i].
The 4 text boxes (containing trigonometric expressions) that appeared at the end of these dynamics represent the lengths of the 4 BOLD SEGMENTS you see in this diagram. [br][br]Drag each expression next to its appropriate segment in this diagram.
Use your results from (3) and (2) to write an expression for [math]tan\left(\alpha-\beta\right)[/math] in terms of these expressions (within the given diagram). [br][br]What do you get?