a sector has area of 15.3 square meters. the radius of the circle is 3 meters.
a. find the radian measure of the central angle
b. find the degree measure of the central angle
c. find the arc length of the sector.
+128408 Area of sector = (1/2)r^2 * (theta in rads )
So
15.3 = (1/2) (3)^2 * ( theta in rads)
15.3 = 9/2 * (theta in rads ) multiply both sides by 2/9
15.3 (2/9) = (theta in rads)
3.4 = theta in rads
To conert this to degrees we have
3.4 * 180° / pi ≈ 194.8°
To find the arc length, S, we have
S = 2 * pi (radius) (194.8 / 360) =
2 * pi * 3 * (194.8 / 360) =
6* ( 194. 8 / 360) * pi ≈ 81.26 m
