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Math Help - Find the Length Of Track.

  1. #1
    Junior Member
    Joined
    Feb 2008
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    Find the Length Of Track.

    Ok final one. I think, possibly I know how to do this.

    Ok question goes sorta like this [summarized]

    An incline that transports passengers back and forth [up and down] a mountain, has an angle elevation of 30 degrees. Angle of elevation to the top of the track from a point horizontal 100 ft from the base which is about 26.8 degrees. What is the lengh of the track?

    Uhm, too lazy to draw the pretty triangle lol.

    On this problem do i just do 180-30-26.8= 123.2

    and carrry it on out by uaing the law of sines ( a / sinblah = b / sinblah )?
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, topaz192!

    You have the right idea, but you need a better diagram.


    An incline that transports passengers up and down a mountain,
    has an angle elevation of 30. From a point horizontal 100 ft from the base,
    the angle of elevation to the top is 26.8.
    What is the lengh of the track?
    Code:
                                          * B
                                      * * |
                                  *   *   |
                              *     *     |
                          *       *       |
                      *         *         |
                  *           *           |
              * 26.8  150 * 30         |
          * - - - - - - - * - - - - - - - *
          D      100      A               C
    We have: . \angle BAC = 30^o \quad\Rightarrow\quad \angle BAD = 150^o

    . . and: . DA = 100,\;\angle D = 26.8^o


    In \Delta BAD,\;\angle DBA \;=\;180^o - 26.8^o - 150^o \;=\;3.2^o

    Law of Sines: . \frac{AB}{\sin26.8^o} \:=\:\frac{100}{\sin3.2^o}


    Therefore: . AB \;=\;\frac{100\sin26.8^o}{\sin3.2^o} \;=\;807.7129786 feet.

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  3. #3
    Junior Member
    Joined
    Feb 2008
    Posts
    74
    Oh ok I sooo get it now! :]
    At first I didnt know how you got 150. But I know now. [180-30]

    Hmmm. No questions here. I finished working all the rest of the problems that relate to this.

    Thank you for your time!!
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