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Math Help - altitude of a tent.

  1. #1
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    altitude of a tent.

    the definition of altitude - a line which passes through a vertex of the triangle and is perpendicular to the opposite side.

    Reflecting at the definition, if I want to imagine the altitude of a tent we would rather measure it from the ground to the top of tent. In the definition of altitude, why do they insist that the line should pass through vertex.
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    Re: altitude of a tent.

    Quote Originally Posted by hisajesh View Post
    Reflecting at the definition, if I want to imagine the altitude of a tent we would rather measure it from the ground to the top of tent. In the definition of altitude, why do they insist that the line should pass through vertex.
    There is no point in re-inventing the wheel. Read this webpage.
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    Re: altitude of a tent.

    @Plato: Thanks for referring this page. I have got another question from the attachmentaltitude of a tent.-altitude.png
    BD is one of the altitudes which passes from the vertex to its opposite side. What about the altitude AB, it passes through the vertex B and it touches another vertex A instead of an opposite side. So, is AB an altitude . Appreciate your patience.
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    Re: altitude of a tent.

    Quote Originally Posted by hisajesh View Post
    attachmentClick image for larger version. 

Name:	altitude.png 
Views:	3 
Size:	4.2 KB 
ID:	29137
    BD is one of the altitudes which passes from the vertex to its opposite side. What about the altitude AB, it passes through the vertex B and it touches another vertex A instead of an opposite side. So, is AB an altitude . Appreciate your patience.
    Any triangle has three altitudes, one for each vertex.
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  5. #5
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    Re: altitude of a tent.

    Hello, hisajesh!

    Definition of altitude:
    a line which passes through a vertex of the triangle and is perpendicular to the opposite side.

    Reflecting at the definition, if I want to imagine the altitude of a tent,
    I would rather measure it from the ground to the top of tent.
    In the definition of altitude, why do they insist that the line should pass through vertex?

    How else would you measure the "height" of a tent?

    Code:
                *
               /:\
              / : \
             /  :h \
            /   :   \
           /    :    \
          *-----*-----*

    Would you consider this to be the height?
    Code:
                *
               / \
              *   \
             /:    \
            / :h    \
           /  :      \
          *---*-------*

    Or this?
    Code:
                *
               / \
              /   \
             /     *
            /     h:\
           /       : \
          *--------*--*
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    Re: altitude of a tent.

    Agree!
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    Re: altitude of a tent.

    Quote Originally Posted by hisajesh View Post
    Click image for larger version. 

Name:	altitude.png 
Views:	3 
Size:	4.2 KB 
ID:	29137
    BD is one of the altitudes which passes from the vertex to its opposite side. What about the altitude AB, it passes through the vertex B and it touches another vertex A instead of an opposite side. So, is AB an altitude .
    Assuming that the enagle B is a right angle - AB is indeeed an altitide, because it starts at one vertex (A) and is perpendicular to the opposite side BC. It happens to be perpendicular at point B, which is alo a vertex, but that's OK. The point is that the definition of an altitude holds for the line AB in this case.
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