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August 18th, 2013, 08:17 AM   #1
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Need assistance with solving a triangle

Hey guys,

Here's a drawing to help illustrate what I'm trying to accomplish:
[attachment=0mil1qpd]circle-solve-01a.png[/attachmentmil1qpd]

Any ideas on how to solve this?
Thanks!

-Kim
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File Type: png circle-solve-01a.png (7.2 KB, 106 views)
covert is offline  
 
August 18th, 2013, 08:40 AM   #2
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Re: Need assistance with solving a triangle

Using the cosine rule you get this.

Do you see how I got to this ?
Can you solve this equation for rC now ?
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August 18th, 2013, 09:10 AM   #3
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Re: Need assistance with solving a triangle

You can reduce "the work" quite a bit with following "short-cuts":

Let the radii = a and b and c .
Since a and b plus angle y are GIVENS, then let u = a+b and v = COS(y)

Then (as shown by my gf Jelly!):
(a + c)^2 = u^2 + (b + c)^2 - 2uv(b + c)

a^2 + 2ac + c^2 = u^2 + b^2 + 2bc + c^2 - 2uvb - 2 uvc

Notice the c^2 on both sides will cancel out: sooooo take over
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August 22nd, 2013, 09:02 AM   #4
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Re: Need assistance with solving a triangle

Thanks guys. Somehow I had forgotten all about solving polynomials ^^
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