Answer:
Explanation:
Given a circle of radius 7 m with central angle AOB = 150°, you want the length of long arc AB and the area of the sector it bounds.
Arc length
The length of an arc of a circle is ...
s = rθ
where θ is the central angle in radians.
Here, the long arc in degrees is 360° -150° = 210°. In radians, that is ...
210° = 210°×π/180° radians = 7π/6 radians
So, the arc length is ...
s = (7 m)(7π/6) = 49π/6 m . . . . arc length
Area
The area of the sector is half the product of the arc length and the radius; (You can think of it as a kind of triangle.)
A = 1/2s·r
A = 1/2(49π/6 m)(7 m) = 343π/12 m² . . . . area