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Triangle trig

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Triangle trig

Post  karooomph on Thu Apr 09, 2009 7:44 pm

In the diagram, triangle ABC is right-angled at C. Also, 2sinB = 3tanA. Determine the measure of angle A.




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Re: Triangle trig

Post  bfrsoccer on Thu Apr 09, 2009 11:27 pm

If a graphing calculator is allowed, you can simply graph 3sin(x) and 2tan(90-x), which intersect in only one place within 0<x<90, x=60. So B=60 degrees and A=90-60=30 degrees.

Otherwise, you have:
B=90-A
2sin(90-A)=3tan(A)
2cos(A)=3tan(B)
2cos(A)=3sin(A)/cos(A)
2cos2(A)=3sin(A)
2(1-sin2(A))=3sin(A)

From here, you can substitute u=sin(A), solve the quadratic equation for u, then take the sin-1 for whatever answer works, and I'm guessing you'll get A=60 degrees.
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Re: Triangle trig

Post  karooomph on Fri Apr 10, 2009 12:21 pm

alrite, some problems here:

2sin(90-A)=3tan(A)
2cos(A)=3tan(B)
-on the left side, how do you change sin to cos like that?

similarly....
2cos2(A)=3sin(A)
2(1-sin2(A))=3sin(A)
-the LS again, what did you do to get that?

3rd: what u?, when you say u=sinA?

and lastly, last line i think you mean A = 30

and those are the only problems i have.
thanks!
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Re: Triangle trig

Post  bfrsoccer on Sun Apr 12, 2009 12:26 am

"on the left side, how do you change sin to cos like that?"->It's a trigonometric identity for sin(a-b)

"-the LS again, what did you do to get that?"

sin2(x) + cos2(x) = 1; identity
1-sin2(x)=cos2(x)

"what u?, when you say u=sinA?" 2(1-sin2(A))=3sin(A)
Literally substitute u=sin(A) into the equation and solve: 2(1-u2)=3u
Then, once you have u, you can find a because you know u=sin(A)

"and lastly, last line i think you mean A = 30" er, oops, yeah, I meant 30
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Re: Triangle trig

Post  karooomph on Sun Apr 12, 2009 5:30 pm

ic now, thanks, bfrsoccer
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Re: Triangle trig

Post  karooomph on Mon Apr 13, 2009 2:43 pm

2cos(A)=3tan(B)
[quote]

I think you meant tan(A).
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Re: Triangle trig

Post  bfrsoccer on Mon Apr 13, 2009 6:35 pm

Oops, yeah, sorry.
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Re: Triangle trig

Post  caseycolin on Mon Aug 02, 2010 5:22 am

yeah, thanks for that.


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Last edited by caseycolin on Wed May 04, 2011 1:40 am; edited 1 time in total

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Re: Triangle trig

Post  LeeRain on Fri Sep 24, 2010 6:47 pm

Hi,
There seems to be a problem with the bbcode for Googlevideo using full URL. Has anyone else noticed this?
I cappied and pasted the BBcode and html replacements in the relevant sections but nothing happens when i insert a video using the bbcode.



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