Kia asked in Science & MathematicsMathematics · 1 decade ago

Trig sectors? Helpppppppppp pleasee?

Help :((

the length of an arc of a circle is 12cm the corresponding sector is 108cm^2 find the radius of the circle and central angle.

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  • 1 decade ago
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    Area of the sector = (Area of circle)*[(arc length)/Circumference]

    Arc length = A

    Area of circle = pi*R^2

    Circumference = 2*pi*R

    Area of the sector = (pi*R^2)*[A/(2*pi*R)]

    Area of the sector = R*A/2

    R = 2*(Area of the sector)/A

    R = 2*108/12

    R = 18 cm

    Angle = (Arc length)/R

    Angle = 12/18 = 2/3 Radians

    Angle = 38.2 degrees

    Ceck by calculating the area of the sector from the radius we found above.

    area of circle = pi*R^2 = 1017.87602

    circumference = 2*pi*R = 113.0973355

    (arc length)/circumference = 12/113.0973355 = 0.106103295

    (area of circle)*(arc length)/circumference = 108

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