Answer: 310.3° or 5.41 radians.
Step-by-step explanation:
The area of a circle of radius R is calculated as:
A = pi*R^2
Now, if we have a sector of an angle θ degrees, the area of that sector is:
A = (θ/360°)*pi*R^2
In this case, we know that:
R = 15yd
And the area of the sector is 609 yd^2
Then we can replace these two values in the equation to get:
609yd^2 =(θ/360°)*3.14*(15yd)^2
(609yd^2)*360°/(3.14*(15yd)^2) = θ = 310.3°
And we want the angle also in radians.
We know that:
3.14 rad = 180°
(3.14 rad/180°) = 1
Then:
310.3° = 310.3°*(3.14 rad/180°) = (310.3°/180°)*3.14 rad = 5.41 radians.
