Math

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1. Find the area of a segment of height 22.1 inches in a circle of radius 6.42 ft. Draw a rough sketch of a circle showing the height and radius. Consider significant digits.

  • Math -

    the perpendicalar to the chord will be 22.1 inches
    and it will meet the chord at its midpoint
    So you have a rightangled triangle with the radius as the hypotenuse 6.42 ft or 77.04 inches
    and shorter sides 22.1 and x
    Use Pythagoras to find the radius

    x^2 + 22.1^2 = 77.04^2

    -use basic trig to find the central angle of the sector
    -use a ration to find the area of the sector
    -find the area of the triangle formed by the chord and the centre of the circle, you know the angle

    Area of whole circle = 70.04^2 π

    subtract the area of the triangle from the area of the sector to find the area of the segment.

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