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Standards/Math/Massachusetts/G-C.B.5

G-C.B.5

G-C.B Find arc lengths and areas of sectors of circles.
G-C.B.5

Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Example Problems
An arc subtends a central angle of 67​π radians. What fraction of the circumference is the arc?
An arc subtends a central angle of 47​π radians. What fraction of the circumference is the arc?
An arc subtends a central angle of 611​π radians. What fraction of the circumference is the arc?
Khan Academy Resources
Arcs, ratios, and radiansChallenge problems: Arc length 1Challenge problems: Arc length 2Challenge problems: Arc length (radians) 2Challenge problems: Arc length (radians) 1Radians & degreesArc lengthArea of a sectorArc measure with equationsArc measureRadians & arc lengthRadians to degreesDegrees to radiansRadians & degreesIntro to radiansArc length from subtended angle: radiansFinding arc measures with equationsArea of a sectorRadians as ratio of arc length to radiusSubtended angle from arc lengthIntro to arc measureArc length from subtended angleArc length as fraction of circumferenceFinding arc measures
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