Exploring Sines: Another Key Triangle Relationship

In the app below, the points A, B, and C are draggable.
In the input bar on the left side, find the values of the following ratios. (See if you can find where the Greek letters are!)[br][br][img width=630,height=191]https://lh4.googleusercontent.com/gwjIPSSjpFX_7ZHTXBOuXcKsmCGpDylNtIHYMYdrQgif4Y7UONh6OSZESxwa9P1Z0fZuQpoq-EfDePc5kbSwGQyEO-JsvY70JJ0jsh7bDdPWjeoL9ru51U2Bc392WG1u1buAZvmz[/img][br]
Now move A, B, and C around in the app above. What do you notice about the values of these ratios? [br][br][img width=630,height=191]https://lh4.googleusercontent.com/gwjIPSSjpFX_7ZHTXBOuXcKsmCGpDylNtIHYMYdrQgif4Y7UONh6OSZESxwa9P1Z0fZuQpoq-EfDePc5kbSwGQyEO-JsvY70JJ0jsh7bDdPWjeoL9ru51U2Bc392WG1u1buAZvmz[/img]
Now move A, B, and C around in the app above. WHAT ELSE do you notice about the values of these ratios? Describe! [br][br][img width=630,height=191]https://lh4.googleusercontent.com/gwjIPSSjpFX_7ZHTXBOuXcKsmCGpDylNtIHYMYdrQgif4Y7UONh6OSZESxwa9P1Z0fZuQpoq-EfDePc5kbSwGQyEO-JsvY70JJ0jsh7bDdPWjeoL9ru51U2Bc392WG1u1buAZvmz[/img]
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Information: Exploring Sines: Another Key Triangle Relationship