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February 6th, 2013, 12:01 AM  #11 
Global Moderator Joined: Dec 2006 Posts: 20,820 Thanks: 2159 
Also, SSA is unambiguous if the side opposite the given angle is longer than the side adjacent to it (use the sine rule).

February 6th, 2013, 05:18 PM  #12 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: find the angles and sides of the triangle
But the SSA is not unique, between the 2 S you can have any angle and so you get many possibilities for the 3rd side and the third angle.

February 7th, 2013, 04:02 AM  #13 
Global Moderator Joined: Dec 2006 Posts: 20,820 Thanks: 2159 
That's incorrect. The number of two possibilities may be 0, 1 or 2, but cannot be greater than 2.

February 8th, 2013, 05:22 PM  #14 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: find the angles and sides of the triangle
Take the angle between the two sides equal to 50, you get one possibility for SSA. Then change the angle say, 30 you will get another one. For almost all angles,there will be a possibility, I think.

February 9th, 2013, 01:14 AM  #15 
Global Moderator Joined: Dec 2006 Posts: 20,820 Thanks: 2159 
Think again.

February 13th, 2013, 05:24 PM  #16 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: find the angles and sides of the triangle
Yes maximum 2. A little thought experiment made me reach this conclusion, but I need to prove it... I will try.

February 14th, 2013, 06:27 PM  #17 
Senior Member Joined: Dec 2012 Posts: 450 Thanks: 0  Re: find the angles and sides of the triangle
1 possibility when the side opposite A is longer. 2 possibilities when the side opposite A is shorter. 1 possibility when the 2S(sides) are equal. And 0 possibility when the triangle can't be drawn, but I cannot say when the triangle cannot be drawn, can anybody? Maybe in cases like the sides are equal, but the angle greater than or equal to 90, right 

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