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    Length of an arc - when will a person leave your view?

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    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Two people 1.8m tall walk from each other until they can no longer see each other (due to the curvature of the earth which has a radius of 6378km).
    Assuming nothing else blocks their view, how far do they have to walk?

    Note. I cant get my head around how this relates to what we've learned about radius and arc length.

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf
    https://brainmass.com/math/curves/length-arc-person-leave-view-15678

    SOLUTION This solution is FREE courtesy of BrainMass!

    Let S be the distance between the two people such that after walking through a distance S, they won't be able to see each other.
    Let R = 6378Km = 6378000 m be the radius of the earth.
    Ler angle ACB = 2Theta (see figure)

    We know that,
    arc length / radius = angle in radians

    Therefore, S/R = 2*theta

    or, S = R * 2*theta ....(1)

    Now, consider the triangle PCB. (The line CP divides S into two equal parts)
    angle PCB = theta
    PC = 6378000 - 1.8 = 6377998.2 m
    CB = 6378000m

    Cos[theta] = base/hypotenuse = 6377998.2/6378000 = 0.9999997
    theta = arc cos[0.9999997] = 0.04 degrees

    converting it to radians using
    180 degree = pi radians
    therefore, 0.04 degrees = pi*0.04/180 = 6.978*10^-4 radians

    Therefore, theta = 6.978*10^-4 radians

    Hence, arc length, S = R * 2 * theta = 6378000 * 2 * 6.978*10^-4
    => S = 8900.85 m
    or S = 8.9 Km

    That is after travelling a distance of 8.9 Km the two persons will not be able to see each other.

    Hope you could follow well. The only concepts we used are the relation of arc length and radius of a circle and the basic trigonometric formulae.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:55 pm ad1c9bdddf>
    https://brainmass.com/math/curves/length-arc-person-leave-view-15678

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