A solution.
[b]Notes:[/b] [list] [*]The values of a, b, c and u, v, w satisfy the algebraic system at the end of the first worksheet. Multiply this equality by s and it converts the algebra of Worksheet 1 into the values used here. But how would we know to use it? The missing step is a shrewd observation: if I figure out the lengths are related by sums and differences of angles, converting the unknowns into a trigonometric expression is a natural next step. If I don't, this step has an air of magic to it. [i]There is no mystery to the solution of mathematical problems.[/i] Set up the problem. Then try to solve it. If you fail over and over and over and over again, you're doing it right, so don't give up. [*]Draw the sin² and cos² of an angle on a diameter: [url]http://www.geogebratube.org/material/show/id/31122[/url] [*]Proof of Heron's Formula: [url]http://www.geogebratube.org/material/show/id/31135[/url] The geometric proof is intimately* related with Malfatti's problem. [/list] _________ *Officially, they're just friends. Whatever. _______ Malfatti's Problem 1. Identify and describe the constraints: [url]http://www.geogebratube.org/material/show/id/32079[/url] [b]→2. Solution[/b] 3. Trig Supplement: [url]http://www.geogebratube.org/material/show/id/31985[/url] These are self-study materials. Let me know how I can make them more useful to you.