Results 1 to 5 of 5

Math Help - TRIPODing along...

  1. #1
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,173
    Thanks
    74

    TRIPODing along...

    A tripod has equal length legs = a.
    It sits on an isosceles triangular base, sides b,b,c.
    It has height = h.

    If the base is changed to sides b,c,c, what is the new height (as an expression)?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by Wilmer View Post
    A tripod has equal length legs = a.
    It sits on an isosceles triangular base, sides b,b,c.
    It has height = h.
    If the base is changed to sides b,c,c, what is the new height (as an expression)?
    It's not clear to me what sort of "expression" you want for the new height.

    The original height h can be calculated in terms of a, b and c. I get the relation h^2 = a^2 - \frac{b^4}{4b^2-c^2}. If the sides of the base are changed from b,b,c to b,c,c, that is equivalent to exchanging b and c. So the new height k would be given by k^2 = a^2 - \frac{c^4}{4c^2-b^2}. You could then derive a (messy) expression for the ratio k/h if that is what you wanted.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Nov 2007
    From
    Trumbull Ct
    Posts
    918
    Thanks
    27
    Hello Wilmer,
    Creating an expression is too messy for me but given a,b,c the triangle which determines the altitude h consists of the following line segments

    A perpendicular bisector of base triangle bbc
    B perpendicular bisector of tripod triangle aac
    C a

    Using the cosine rule the angle between a and A can be determined. If this angle is K h =asinK


    bjh
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Dec 2007
    From
    Ottawa, Canada
    Posts
    3,173
    Thanks
    74
    Merci BJ.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Quote Originally Posted by bjhopper View Post
    Creating an expression is too messy for me but given a,b,c the triangle which determines the altitude h consists of the following line segments

    A perpendicular bisector of base triangle bbc
    B perpendicular bisector of tripod triangle aac
    C a

    Using the cosine rule the angle between a and A can be determined. If this angle is K h =asinK
    Another method is to say that the sphere of radius a, centred at the top of the tripod, contains all three vertices of the triangle and hence contains its whole circumcircle. If the radius of the circumcircle is r, you then have a right-angled triangle with sides a (hypotenuse), r and h. I used the formula for the circumradius, together with Pythagoras, to get the expression for h.
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum