Trig sectors? Helpppppppppp pleasee?
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.
- Captain MephistoLv 71 decade agoFavorite Answer
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