Pre Calculus trigonometry

Question

What is the central angle measure (inradians) if the area of a sector is 1200m², and the radius is 20m? 

Answer 1

radius = 20 m = r

sector area = 1200 m^2 = A

central angle = 6 radians

central angle = 2A/r^2 = 2(1200)/400 = 6 radians

a circle has 2pi radians = about 2(3.14) = 6.28 radians

the central angle is nearly a full circle, almost 360 degrees

a circle's area = pi(r^2) = pi(20)^2 = 400pi = about 400(3.14) = 1256 m^2

one radian = 180/pi degrees

6(180)/pi = 1080/pi = about 1080/3.14 = 344 degrees,

a full circle is 360 degrees

sector area = 6(r^2)/2 = 6(400)/2 = 1200 square meters

Answer 2

A = r²θ / 2