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February 14th, 2009, 09:44 AM  #1 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  How can I calculate the lengths of all 3 sides?
If I have a right angled triangle, and I know the other two angles and the area of the triangle, how can I calculate the lengths of all 3 sides? Something tells me the answer is quite simple, but I'm stumped. It's driving me crazy.

February 14th, 2009, 10:16 AM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: How can I calculate the lengths of all 3 sides?
If a triangle has sides a,b and c with the angles opposite each side given by respectively, then the area A is given by In the case of a right angled triangle, one of the angles  say  is a right angle, so and This means that so the expression (where a is the hypotenuse) becomes Rearrange to find a,b and c. 
February 14th, 2009, 10:23 AM  #3 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Re: How can I calculate the lengths of all 3 sides?
Thanks so much for that! It really was driving my nuts. I was actually half way there and confused myself. 
February 14th, 2009, 03:47 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,275 Thanks: 516  Re: How can I calculate the lengths of all 3 sides? Quote:
Q=ab/2. sinA/a = sinB/b. Therefore Q=[sinB/(2sinA)]a^2  
February 14th, 2009, 07:07 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 17,719 Thanks: 1359  
February 14th, 2009, 09:16 PM  #6 
Member Joined: Feb 2009 Posts: 34 Thanks: 0  Re: How can I calculate the lengths of all 3 sides?
actually you don't need but a single angle and you find those sides

February 16th, 2009, 04:21 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 17,719 Thanks: 1359 
No, you started with a single angle (the right angle) and the area. You need another angle to allow the sides to be found.


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