Interact with the applet below for a minute. [br]Then, answer the questions that follow. [br](Please don't slide the 2nd slider until prompted to in the directions below.)
1) Take a look at the yellow right triangle on the left.[br]Write an equation that expresses the relationship among angle [i]B[/i], the triangle's height, and side [i]c[/i].
Hint: Consider using a trigonometric ratio.
2) Rewrite this equation so that [i]height [/i]is written in terms of side [i]c[/i] and angle [i]B[/i].
3) Now consider the pink right triangle on the right. Write an equation that expresses the relationship among angle [i]C[/i], side [i]b[/i], and the triangle's height. [br]
Hint: Refer to hint for first question!
4) Rewrite this equation so that [i]height[/i] is written in terms of side [i]b[/i] and angle [i]C[/i].
5) Take your responses to questions (2) and (4) to write a new equation that expresses the relationship among [i]C[/i], [i]B[/i], [i]c[/i], and [i]b[/i]. Write this equation so that [i]C[/i] and [i]c[/i] appear on one side of the equation and that [i]B[/i] and [i]b[/i] appear on the other.
6) Now drag the slider in the upper right hand corner. Now, given the fact that the length of segment [i]BC[/i] would be denoted as [i]a [/i](it's just not drawn in the applet above), write an expression for the area of this original triangle in terms of [i]a[/i], [i]b[/i], and [i]C[/i].
7) Same question as in (6) above, but this time write the area of the triangle in terms of [i]a[/i], [i]c[/i], and [i]B[/i].
8) Suppose that dragging the first slider dropped a height from point [i]C[/i] instead of point [i]A[/i]. Answer questions (1) - (5) again, this time letting [i]c[/i] serve as the base of this triangle (vs. side [i]a[/i]). Notice anything interesting in your results?