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  1. #1
    Senior Member euclid2's Avatar
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    word problem

    Vivian and Bobby are 250m apart and are facing each other. Each one is
    looking up at a hot air balloon. The angle of elevation from Vivian to the
    balloon is 75 and the angle of elevation from Bobby to the balloon is 50.
    Determine the height of the balloon, to one decimal place.
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  2. #2
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    let Viv be a horizontal distance x to a point directly beneath the balloon.
    Bob is (250-x) from the same point.

    extend a perpendicular vertically downward from the balloon to the ground ... let that vertical distance = h.

    note also that two right triangles are formed ... one for Viv, one for Bob.

    using Viv's triangle, h/x = tan(75)

    using Bob's triangle, h/(250-x) = tan(50)

    you now have two equations with two unknowns ... your goal is to find the value of h.
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  3. #3
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    Hello, euclid2!

    I like skeeter's solution . . . Here's my version.


    Vivian and Bobby are 250 m apart and are facing each other.
    Each one is looking up at a hot air balloon.
    The angle of elevation from Vivian to the balloon is 75
    and the angle of elevation from Bobby to the balloon is 50.
    Determine the height of the balloon, to one decimal place.
    Code:
                  H
                  *
                 *: *
                * 55 *
               *  :     *  v
              *   :       * 
             *    :y        *
            *     :           *
           * 75  :        50  *
        V *   *   *   *   *   *   * B
                 h = 250

    We have: . VB = h = 250
    Since \angle V = 75^o,\;\angle B = 50^o, we have: . \angle H = 55^o
    And we want y.


    Law of Sines: . \frac{v}{\sin V} = \frac{h}{\sin H} \quad\Rightarrow\quad v \:=\:\frac{250\sin75^o}{\sin55^o} \:\approx\:294.8

    We have: . \sin B = \frac{y}{v}\quad\Rightarrow\quad y \:=\:v\!\cdot\!\sin B \:=\:294.8\sin50^o \;=\;\boxed{225.8\text{ m}}

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  4. #4
    Senior Member euclid2's Avatar
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    Thanks very much
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