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February 14th, 2009, 09:44 AM   #1
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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.
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February 14th, 2009, 10:16 AM   #2
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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.
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February 14th, 2009, 10:23 AM   #3
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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.
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February 14th, 2009, 03:47 PM   #4
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Re: How can I calculate the lengths of all 3 sides?

Quote:
Originally Posted by SecretSamurai
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.
Here is a simpler approach: a,b,c be sides A and B angles opposite a and b (c is hypotenuse). Q=area.

Q=ab/2. sinA/a = sinB/b. Therefore Q=[sinB/(2sinA)]a^2
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February 14th, 2009, 07:07 PM   #5
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February 14th, 2009, 09:16 PM   #6
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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
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February 16th, 2009, 04:21 AM   #7
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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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