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math

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angle of elevation of the top of a mountain to a man is 45degree.if we walk along a slope of 30 degree of the mountain 100 meters then the angle of elevation of the top of mountain becomes 60 degree.find the height of the mountain.

  • math - ,

    The line of sight of 45 deg angle is
    drawn as the hyp. of a rt triangle.
    The ht. of the mountain is the ver. side of the triangle. the hor. side
    side = 100 + X. The line of sight of the 60 deg. angle represents the hyp.
    of a 2nd triangle and the ht. of the
    mountain is the ver. side of both triangles.

    Tan(45) = h /(100+X),
    h = (100 + X) * Tan(45),
    .
    Tan(60) = h / X,
    h = x * Tan(60).

    h = (100 + X) * Tan(45) = X * Tan(60),
    Solve for X:
    70.7 + 0.707X = 1.73X,
    - 1.73X + 0.707X = - 70.7
    X = 69 METERS.
    h = 69 * TAN(60) = 119.5 Meters =
    ht. of mountain.

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