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Math Help - Find the angle in a Tetrahedron

  1. #1
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    Find the angle in a Tetrahedron

    The point P is the midpoint of the altitude of the regular Tetrahedron. P is linked with A , B of the base of Tetrahedron with segments PA and PB.
    Find the angles between these segments.
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  2. #2
    Member Nacho's Avatar
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    Find the angle in a Tetrahedron-aaaaaaaaaaaaaaaaaaaa.png

    We say tha size of each one triangule is l, now AC=CF=CB hence <br />
CB = \frac{{l\sqrt 3 }}<br />
{3} \Rightarrow DC = \frac{{l\sqrt 6 }}<br />
{3} \Rightarrow PC = \frac{{l\sqrt 6 }}<br />
{6}<br />

    for other size

    <br />
PC^2  + CB^2  = PB^2  \Rightarrow PB = \frac{{\sqrt 2 l}}<br />
{2}<br />

    but: <br />
\sin \alpha  = \frac{{GB}}<br />
{{PB}} = \frac{{\frac{l}<br />
{2}}}<br />
{{\frac{{\sqrt 2 l}}<br />
{2}}} = \frac{{\sqrt 2 }}<br />
{2} \Rightarrow \alpha  = \frac{\pi }<br />
{4} \Leftrightarrow \measuredangle APB = \frac{\pi }<br />
{2}<br />
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  3. #3
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    Quote Originally Posted by Nacho View Post
    Click image for larger version. 

Name:	aaaaaaaaaaaaaaaaaaaa.png 
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    is this a regular tetrahedron ?
    i thought that a regular tetrahedron is a regular 3 sides pyramid
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  4. #4
    Member Nacho's Avatar
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    Quote Originally Posted by beq!x View Post
    is this a regular tetrahedron ?
    i thought that a regular tetrahedron is a regular 3 sides pyramid
    Tetrahedron - Wikipedia, the free encyclopedia
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