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Math Help - Heights and distance problem

  1. #1
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    Heights and distance problem

    The angle of elevation from a point(on ground) is 45 degree and after 20 seconds its 30 degree If the aircraft is flying at a constant speed at 360 km/h. Find the height of plane from the ground.

    I tried to solve the problem. The answer is 2000\sqrt{3}. Please help.
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  2. #2
    Senior Member Sambit's Avatar
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    Follow the link http://img684.imageshack.us/img684/8819/unledaj.png

    angle AOB=45, angle COD=30. AB=CD, CA=DB. A is the initial position of the plane; and C is the position of the plane after 20 seconds. In 20 seconds, the plane covers a distance of 2000 mitres. So AC=2000.

    tan(AOB)=tan(45)=1=AB/BO. So AB=BO

    tan(COD)=tan(30)=1/sqrt(3)=CD/DO=CD/(DB+BO)=CD/(2000+BO)=AB/(2000+BO)=AB/(2000+AB)

    That is AB/(2000+AB) = 1/sqrt(3)

    Solving, AB = 2000/{sqrt(3)-1} which is the required height.

    EDIT: In case the above link is non-accessible, here is another link http://oi56.tinypic.com/2eldz4n.jpg
    Last edited by Sambit; May 3rd 2011 at 08:11 AM. Reason: extra link added
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  3. #3
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    Hello, vivek_master146!

    The angle of elevation of a plane from a point on ground is 45 degree
    and after 20 seconds it's 30 degrees.
    If the plane is flying at a constant speed at 360 km/h, find the altitude of plane .

    The answer is 2000√3. . Wrong!
    Code:
                      A
                      *
                    * |
                  *   |
                *     |h
              *       |
            * 45d     |
        O * - - - - - *B
                h



    Code:
                      A     2     C
                      . - - - - - *
                    . .       *   |
                  .   .   *       |
                .     *h          |h
              .   *   .           |
            . * 30d   .           |
        O * - - - - - * - - - - - *
                 h _  B     2     D
          : - - - √3h - - - - - - :


    . .







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