Geometry: "Angles correspond to their opposite sides."

[garg.arika]

Hello, I have a follow-up question to one of the concepts in the Geometry Strategy Guide (Guide 5, Fourth Edition), on page 27: "Angles correspond to their opposite sides." While I understand the concept being explained, I want to know whether what seems (to me) to be a logical extension of this concept is actually correct:

If you have a triangle, and you know the lengths of two of its sides--8 and 12--and you know that the angle opposite the side that has a length of 8units is 30degrees, can you essentially find the values of all the other sides and all the other angles?

So for example, can I conclude that the angle opposite the side that has a length of 12 is 30/8*12 = 45 degrees? I can then find the third angle: 105 degrees. And then I can use the fact that "angles correspond to their opposite sides" to find the length of the remaining side of the triangle. Is that correct?

Thanks for your help!

[tim]

no, you can't take this concept quite that far. all the rule tells you is the relative size of the angles. if the angle opposite 8 is 30 degrees, you know that the angle opposite 12 is larger than 30 degrees. you won't be able to calculate the size of the angle directly..