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Thread: theorem 7.3

  1. #1
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    theorem 7.3

    i have to find out if the triangle is acute obtuse or right, the problem gives me three numbers and no image. can someone help me out ?
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    Re: theorem 7.3

    Quote Originally Posted by Kirstenspears View Post
    i have to find out if the triangle is acute obtuse or right, the problem gives me three numbers and no image. can someone help me out ?
    If the numbers are a,~b,~\&~c is possible that
    \\c^2=a^2+b^2 \\ a^2=b^2+c^2\\\text{ or }\\b^2=a^2+c^2

    It will be a right triangle.
    .
    Last edited by Plato; Mar 19th 2013 at 01:58 PM.
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  3. #3
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    Re: theorem 7.3

    What "three numbers"? The three side lengths? The three angles? Two angles and a side length? ....


    Assuming, like Plato, that you mean the three side lengths, then think about the "triangle inequality": if the three side lengths are a, b, and c and the opposite angles are A, B, C, respectively, c^2= a^2+ b^2- 2abcos(C) so that if 2abcos(C)= a^2+ b^2- c^2. The angle C is acute if cos(C) is positive, right if cos(C)= 0, and obtuse if cos(C)< 0. And, since a and b, as lengths, are positive, the sign of cos(C) is the same as the sign of a^2+ b^2- c^2. If c^2= a^2+ b^2 then C is a right angle, if c^2> a^2+ b^2 then C is obtuse, if c^2< a^2+ b^2 then C is acute. To tell whether the triangle is acute, right, or obtuse. If you find than any one angle is obtuse or right, then the triangle is obtuse or right. If you find that all three angles are acute, then the triangle is acute.
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