Central Angles & Their Measures

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Presentation transcript:

Central Angles & Their Measures Sector Arc Central Angle

Intercepted Arc of a Central Angle = Measure of Angle ·Radius Arc = rØ˚ where r = radius & Ø˚= central angle Measure of Central Angle Ø˚ = •360˚ (and then multiply by IF they want answer in radians OR ) Area of Sector = or

Ex: Given the measure of a central angle is π/6, find the measure of the intercepted arc (in terms of π) in a circle of radius 10 cm. Ex: This time, the central angle is 10˚ and the diameter is 60 in. 10˚•30 = 300 which in terms of π is: 300• π or 1 180 5 π in. 3

Ex: Given the measure of an arc is 87 cm, find the degree measure (to nearest tenth) of the central angle in a circle of radius 16 cm. Arc measure 360 Circumference Central Angle= 87 360 2•π•16 311.5˚

Ex: Find the area of the sector (to nearest tenth) if the central angle is π⁄6 and radius is 14 cm. Area of sector= Central Angle  πr2 which is 2π 51.3 cm2