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Thread: Right angle triangle

  1. #1
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    Right angle triangle

    Why the other angles in Right angle triangle can't be more than 90 degrees?
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  2. #2
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    Re: Right angle triangle

    It is a basic theorem in Euclidean geometry that the measure of the angles in any triangle sum to 180 degrees ($\displaystyle \pi$ radians). Since a right angle has, by definition, a measure of 90 degrees. That means that the measures of the other two angles must sum to 90 degrees. Since an angle in a triangle cannot have measure 0, that means the other two angles in a right triangle must measure less than 90 degrees each.

    (This is, as I said, in Euclidean geometry. In "spherical geometry", for example, on the surface of a sphere, say the earth, the "prime meridian" through Greenwich, England, from the north pole to the equator, the 90 degrees east longitude, from the north pole to the equator, and the equator forms a "spherical triangle" in which all three angles are right angles.)
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  3. #3
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    Re: Right angle triangle

    Quote Originally Posted by policer View Post
    Why the other angles in Right angle triangle can't be more than 90 degrees?
    Is that a serious question?
    Are you a student attending math classes?
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  4. #4
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    Re: Right angle triangle

    A student ask me the question and I can't answer him correctly, so I ask it here. (!)
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  5. #5
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    Re: Right angle triangle

    ...and my grand-mother can run the mile under 4 minutes...
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