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June 14th, 2010, 04:45 PM   #1
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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?
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June 14th, 2010, 05:15 PM   #2
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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 ?
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June 14th, 2010, 05:36 PM   #3
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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)?
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June 14th, 2010, 06:36 PM   #4
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Angle ABD = 2x - x = x.
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June 15th, 2010, 06:40 AM   #5
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Re: Trigonometry, finding angle when only one side length known

Hello, lesterxburnham!

Quote:


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.










[color=beige]. . [/color]



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June 15th, 2010, 09:31 AM   #6
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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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