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Math Help - Horizontal Distance

  1. #1
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    Horizontal Distance

    At Mogulís Ski Resort, the beginnerís slope is inclined at an angle of 12.3o while the advanced slope is inclined at an angle of 26.4o If Rudy skis 1,000 meters down the advanced slope while Valerie skis the same distance on the beginnerís slope, how much longer was the horizontal distance that Valerie covered?

    (1) 81.3 m (3) 895.7 m
    (2) 231.6 m (4) 977.0 m
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  2. #2
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    Hello, symmetry!

    At Mogulís Ski Resort, the beginnerís slope is inclined at an angle of 12.3į
    while the advanced slope is inclined at an angle of 26.4į.
    If Rudy skis 1,000 meters down the advanced slope
    while Valerie skis the same distance on the beginnerís slope,
    how much longer was the horizontal distance that Valerie covered?

    (1) 81.3 m . . (2) 231.6 m . . (3) 895.7 m . . (4) 977.0 m
    Code:
                                                      *
                                                    * :
                                                  *   :
                              *            1000 *     :
                          *   :               *       :
                 1000 *       :             *         :
                  *           :           *           :
              * 12.3į         :         * 26.4į       :
          * - - - - - - - - - *       * - - - - - - - *
                    V                          R

    The first triangle represents the beginner's slope.
    . . Let V = Valerie's horizontal distance.
    We see that: . \cos12.3^o \;=\;\frac{V}{1000}\quad\Rightarrow\quad V \;=\;1000\cdot\cos12.3^o \;=\;977.0455744

    The second triangle represents the advanced slope.
    . . Let R = Rudy's horizontal distance.
    We see that: . \cos26.4^o \;=\;\frac{R}{1000}\quad\Rightarrow\quad R\;=\;1000\cdot\cos26.4^o \;=\;895.7117602

    The difference is: . 977.0455744 - 895.7117602 \;\approx\;81.3\text{ m} . . . answer (1)

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  3. #3
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    ok

    I had no idea trigonometry was needed to solve this question.

    Thanks!
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