Results 1 to 5 of 5

Math Help - Tetrahedron

  1. #1
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591

    Tetrahedron

    I have attached the question. about the terahedron

    part i) I had no problem with i got the volume as \frac{1}{6} abc

    for part ii) i use Pythagorus theorem to get the lengths of sides CA CA and AB then just used the cosine rule.

    I am just stuck on the last part about the perpendicular distance.

    Thanks, Bobak
    Attached Thumbnails Attached Thumbnails Tetrahedron-picture-1.png  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    For the last part think of the triangle as a plane. Express its equation in the form Ax+By+Cz+D=0. Then the distance is given by the distance formula between this plane and (0,0,0).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    Quote Originally Posted by ThePerfectHacker View Post
    For the last part think of the triangle as a plane. Express its equation in the form Ax+By+Cz+D=0. Then the distance is given by the distance formula between this plane and (0,0,0).
    That worked a treat, I used the formula outlined here Equation of a plane

    however my only concern is that the question is aimed at students who are not familiar with plane geometry. I worried i missed something, can this be done another way ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by bobak View Post
    That worked a treat, I used the formula outlined here Equation of a plane

    however my only concern is that the question is aimed at students who are not familiar with plane geometry. I worried i missed something, can this be done another way ?
    Let a_{ABC} denote the area of the base triangle.
    Use the hint: If you already know the volume of the tetrahedron then you can calculate the height by:

    V=\frac13 \cdot a_{ABC} \cdot h~\implies~ \boxed{h=\frac{3V}{a_{ABC}}}
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Oct 2007
    From
    London / Cambridge
    Posts
    591
    Quote Originally Posted by earboth View Post
    Let a_{ABC} denote the area of the base triangle.
    Use the hint: If you already know the volume of the tetrahedron then you can calculate the height by:

    V=\frac13 \cdot a_{ABC} \cdot h~\implies~ \boxed{h=\frac{3V}{a_{ABC}}}
    Very neat, now the first two parts make a lot more sense.

    Thanks

    Bobak
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Tetrahedron
    Posted in the Statistics Forum
    Replies: 4
    Last Post: January 7th 2010, 07:21 AM
  2. tetrahedron,
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 14th 2009, 02:09 AM
  3. tetrahedron
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 8th 2009, 01:35 PM
  4. tetrahedron 2
    Posted in the Calculus Forum
    Replies: 2
    Last Post: June 29th 2008, 08:21 PM
  5. tetrahedron
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 29th 2008, 03:26 PM

Search Tags


/mathhelpforum @mathhelpforum