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Math Help - Ok, what am I doing wrong??

  1. #1
    Member classicstrings's Avatar
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    Ok, what am I doing wrong??

    Find the area of the minor segment formed on an arc of length 36cm drawn on a circle of radius 50cm.

    Chord length = 2rsin(theta/2)
    2 * 50sin(theta/2) = 36
    theta = 0.7365

    Area of segment = 0.5r^2(theta-sintheta)
    = 81.01cm^2

    Correct answer = 75.77cm^2
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  2. #2
    MHF Contributor

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    I get theta to be 0.72 or 36/50.
    Using that value the area is 75.769.
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  3. #3
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    Hello, classicstrings!

    Find the area of the minor segment formed on an arc of length 36cm
    drawn on a circle of radius 50cm.

    Why are you playing with a chord?
    Code:
                   36
                  * * *
              *           *
           *                 *
          * - - - - - - - - - *
            \               /
              \           /
                \       / 50
                  \ θ /
                    *

    Arc length formula: .s .= .

    We have: .s = 36, r = 50

    . . Hence: .36 = 50θ . . θ = 0.72 (radians)


    Area of a sector: .A .= .

    . . We have: . A .= .(50)(0.72) .= .900 cm


    Area of triangle: .(50)sin(0.72) . .824.23 cm


    . . Therefore: .Area of segment .= .900 - 824.23 .= .75.77 cm


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