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March 2nd, 2013, 06:08 PM  #1 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Find all the sides of this triangle.
[attachment=0:1rwvoeut]untitled5.JPG[/attachment:1rwvoeut] CQ=6cm,QB=8cm Find all other sides of the triangle. If you have solution or progress PM me or hide it here someway.... I am testing the approach of different people.... 
March 2nd, 2013, 06:55 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,785 Thanks: 707  Re: Find all the sides of this triangle.
They depend on the radius, which hasn't been given.

March 2nd, 2013, 06:58 PM  #3 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: Find all the sides of this triangle.
Oh sorry, I forgot it. Ok the radius is 4cm....

March 3rd, 2013, 02:08 PM  #5 
Senior Member Joined: Sep 2010 Posts: 221 Thanks: 20  Re: Find all the sides of this triangle.
The sides are AC=18; AB=20. I can post a solution if needed. 
March 3rd, 2013, 03:53 PM  #6 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: Find all the sides of this triangle.
Ok,post it then.... Sorry,no,no PM me.....Let me see your approach. 
March 4th, 2013, 12:56 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 20,805 Thanks: 2150 
McPogor slipped up.

March 4th, 2013, 07:01 AM  #8 
Senior Member Joined: Sep 2010 Posts: 221 Thanks: 20  Re: Find all the sides of this triangle.
Here's succession of steps. 1)CQ=CR=6; QB=BP=8; AR=AP=x. 2)OC=Sqrt[QC^2+OQ^2]=Sqrt{36+16]=2Sqrt13 OB=Sqrt[QB^2+OQ^2]=Sqrt[64+16]=4Sqrt5. 3)Sin(C/2)=OQ/OC=2/Sqrt13; Sin(B/2)=OQ/OB=1/Sqrt5. 4)Cos(C/2)=Sqrt[1sin^2(C/2)]=3Sqrt(1/13); Cos(B/2)=Sqrt[1Sin^2(B/2)]=2Sqrt(1/5). 5)SinC=2Sin(C/2)Cos(C/2)=12/13; SinB=2Sin(B/2)Cos(B/2)=4/5. 6)AC/SinB=AB/SinC; (6+x)/(4/5)=(8+x)/(12/13). 5(6+x)=13(8+x)/3. Eventually x=12. AC=6+12=18; AB=8+12=20. 
March 4th, 2013, 07:40 AM  #9  
Global Moderator Joined: Dec 2006 Posts: 20,805 Thanks: 2150  Quote:
 
March 4th, 2013, 10:16 AM  #10 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Re: Find all the sides of this triangle.
triangle sides 141820 has area 122.376.... your triangles AOC + AOB + BOC = 36 + 40 + 28 = 104 Sooooo...................listen to Skip If AC = b, then triangle ABC has sides 14, b and b+2 

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