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June 14th, 2010, 04:45 PM  #1 
Newbie Joined: Jun 2010 Posts: 14 Thanks: 0  Trigonometry, finding angle when only one side length known
Hi everyone, I run into following problem: Figure illustrates Triangles ABC and BDC where C is a right angle, AC=17cm and DC=6cm. Given angle BDC = 2x and angle BAD = x, find x. I cannot find solution, I have tried Pythagorean theorem cot^2(x)+1=cosec^2(x) and I ended up with 289/BC + BC = BC^4+34BC^2+289 where I have no clue how to continue that. I also tried BC = 17tan(x) = 6tan2(x) and again didn't find solution. Can you please help me? 
June 14th, 2010, 05:15 PM  #2 
Senior Member Joined: Feb 2010 Posts: 704 Thanks: 138  Re: Trigonometry, finding angle when only one side length known
The answer is x = 28.47213442457299779465217033046743894005698630301 79190093760352286477414715453273837029511364458721 6528734401286968... Would it help to know that AD = DB = 11 ? 
June 14th, 2010, 05:36 PM  #3 
Newbie Joined: Jun 2010 Posts: 14 Thanks: 0  Re: Trigonometry, finding angle when only one side length known
it certainly does help, but I still don't understand why is that (AD=DB)?

June 14th, 2010, 06:36 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,389 Thanks: 2015 
Angle ABD = 2x  x = x.

June 15th, 2010, 06:40 AM  #5  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Trigonometry, finding angle when only one side length known Hello, lesterxburnham! Quote:
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June 15th, 2010, 09:31 AM  #6 
Newbie Joined: Jun 2010 Posts: 14 Thanks: 0  Re: Trigonometry, finding angle when only one side length known
thank you so much for explanation, soroban and thank you all for help! 

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