trigonometry

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An observer at A looks due north and sees a meteor with an angle of elevation of 70deg. At the same instant, another observer 30miles east of A, sees the same meteor and apprroximates its position as N 50deg W but fails to note its angle of elevation. Find the height of the meteor and its distance form A.

  • trigonometry -

    The line of sight of the 2nd observer
    is represented by the hypotenuse of a rt triangle, and the height of the
    meteor is represented by the ver. side
    of the rt triangle.The acute angle bet.
    ween the ver. side and hyp. = 50 deg.
    The angle of elevation is equal to the
    other acute angle or 40 deg.

    Tan(40) = h/30,
    h =30*Tan(40) = 25.2 =height of
    meteor

    Tan(70) = 25.2 / d,
    d = 25.2/Tan(70) = 9.2 = distance of
    meteor.

  • trigonometry -

    CORRECTION!!
    Sin(70) = 25.2/d,
    d = 25.2/Sin(70) =26.8.

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