Results 1 to 4 of 4

Math Help - isosceles trapezoid help

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    2

    isosceles trapezoid help

    Old guy here who's forgotten everything and needs some help.

    I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches. The sides come in with a 6 degree pitch (84 degree angles). What I'm trying to figure out is the length of the top section that parallels the base. I don't have a clue...

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,829
    Thanks
    123
    Quote Originally Posted by cluap View Post
    Old guy here who's forgotten everything and needs some help.

    I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches. The sides come in with a 6 degree pitch (84 degree angles). What I'm trying to figure out is the length of the top section that parallels the base. I don't have a clue...

    Thanks!
    1. Draw a rough sketch. (see attachment)

    2. t = 26- 2x

    3. Use the tan-function in the small right triangles:

    \tan(84^\circ)=\dfrac{16}x~\implies~x=\dfrac{16}{\  tan(84^\circ)} \approx 1.681667764...

    4. Therefore \boxed{t \approx 22.63666447...}
    Attached Thumbnails Attached Thumbnails isosceles trapezoid help-isoscelestrapez.png  
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,658
    Thanks
    598
    Hello, cluap!

    This requires some Trigonometry.
    I hope you're prepared.


    I'm trying to make an isosceles trapezoid with a base of 26 inches and an altitude of 16 inches.
    The sides come in with a 6 (84 ngles).
    What I'm trying to figure out is the length of the top section that parallels the base.
    Code:
                  B     x     C
                  * - - - - - *
                 /|           |\
                / |           | \
               /6|           |  \
              /   |16         |   \
             /    |           |    \
            /     |           |     \
           / 84  |           |      \
        A * - - - * - - - - - * - - - * D
              a   E     x     F   a
          : - - - - -  26 - - - - - - :

    We have isosceles trapezoid ABCD.
    The base is: . AD = 26.
    The height is: . BE = 16

    Let: . x \:=\:BC \:=\:EF
    Let: . a \:=\:AE \:=\:FD

    Then: . a + x + a \:=\:26 \quad\Rightarrow\quad x \:=\:26 - 2a
    . . Hence: . BC \:=\:x \:=\:26 - 2a .[1]


    In right triangle BEA\!:\;\;\tan6^o \:=\:\frac{a}{16} \quad\Rightarrow\quad a \:=\:16\tan6^o \:\approx\:1.68

    Substitute into [1]: . BC \:=\:26-2(1.68) \;=\;22.64\text{ inches}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2009
    Posts
    2
    Guys - I'm sorry... I forgot to save the link, and I couldn't find this place again! Thanks for the help - you answered my questions in a way I could understand! Thanks for your help.

    Take care, Paul
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Isosceles trapezoid problem
    Posted in the Geometry Forum
    Replies: 36
    Last Post: December 15th 2010, 08:40 AM
  2. [SOLVED] isosceles trapezoid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: January 24th 2010, 11:10 PM
  3. Area of Isosceles Trapezoid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 04:44 PM
  4. Area of an Isosceles Trapezoid
    Posted in the Math Topics Forum
    Replies: 3
    Last Post: December 4th 2007, 06:52 AM
  5. isosceles trapezoid
    Posted in the Geometry Forum
    Replies: 1
    Last Post: June 26th 2007, 02:56 PM

Search Tags


/mathhelpforum @mathhelpforum