Results 1 to 6 of 6

Math Help - Determining an exact expression for a length.

  1. #1
    Member
    Joined
    Nov 2009
    Posts
    171

    Determining an exact expression for a length.

    A truss is used to hold up a heavy sign on a building, as shown.



    The truss is attached to the building along side AB, which measures 2.4m. Determine an exact expression for the length CD.

    Answer:



    My progress:

    I found out that side a is approximately 1m. What the heck is going on with that expression though?
    Last edited by kmjt; December 5th 2009 at 11:31 PM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    From your trigonometric functions, you can say that :

    tan(45) = \frac{AB}{BD}, so BD = \frac{AB}{tan(45)} = \frac{2.4}{1} = 2.4

    And also, of course :

    tan(60) = \frac{AB}{BC}, so BC = \frac{AB}{tan(60)} = \frac{2.4}{\sqrt{3}}

    Now, you know that CD = BD - BC, so CD = 2.4 - \frac{2.4}{\sqrt{3}} ( \approx 1.014)

    \rightarrow How did you find your result ? It might be interesting to see your reasoning
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Jul 2009
    From
    Melbourne
    Posts
    274
    Thanks
    4
    edit: Bacterius beat me to it.. oh well


    Well I got my exact value and the answer is same as the one you provided. Here's how I did it:

    To find CD you need to find BC and BD. Then subtract BC from BD.

    You don't even need a calculator for this..

    Set up the BD triangle and ignore the diagonal line through the middle.

    The angle is 45 and we need to find the adjacent.

    tan ratio:

    \tan 45 = \frac {2.4}{x}

    In this equation  x = BD

     x = \frac {2.4}{\tan 45}

    We know that tan45 is 1 so...

     x = 2.4


    Now do the BC triangle..

    The angle is 60 and you need to find adjacent.

    Use tan again:

    \tan 60 = \frac {2.4}{x}

    x = \frac {2.4}{\tan 60}

    We should know that tan60 is \sqrt 3

    So x = \frac {2.4}{\sqrt 3}


    So just put it together...

     2.4 - (\frac {2.4}{\sqrt 3}) = CD

    that's how i did it?
    Last edited by jgv115; December 6th 2009 at 02:31 PM.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by jgv115 View Post
    edit: Bacterius beat me to it.. oh well
    Sorry
    I forgot to mention that triangle ADB is rectangle in B (it is written on the picture but it is better to mention it).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Nov 2009
    Posts
    171
    Thank you both. Btw I got 1 by first finding the length of AC then using that to find the length of DC using sin law. I've got what I need this question is so easy.. thanks
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Super Member Bacterius's Avatar
    Joined
    Nov 2009
    From
    Wellington
    Posts
    927
    Quote Originally Posted by kmjt View Post
    Thank you both. Btw I got 1 by first finding the length of AC then using that to find the length of DC using sin law. I've got what I need this question is so easy.. thanks
    Yeah that's a way too ..
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: August 8th 2011, 02:50 PM
  2. Determining exact values for non-special angles
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: November 2nd 2010, 08:38 PM
  3. Replies: 3
    Last Post: November 28th 2009, 07:06 PM
  4. exact length of curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 8th 2009, 11:38 PM
  5. Determining the exact value of each expression
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: October 23rd 2008, 07:35 PM

Search Tags


/mathhelpforum @mathhelpforum