Answer:
23.7°
9.1~ft
Step-by-step explanation:
Formula for the area of a sector of central angle n (in degrees) and radius r:
[tex] A = \dfrac{n}{360^\circ}\pi r^2 [/tex]
We have:
A = 100 ft^2
r = 22 ft
We need to find:
r
[tex] 100 = \dfrac{n}{360^\circ}\pi (22^2) [/tex]
[tex] n = 23.7^\circ [/tex]
The central angle measures 23.7°.
Formula for the length of an arcs of a circle with central angle n (in degrees) and radius r:
[tex] s = \dfrac{n}{360^\circ}2 \pi r [/tex]
We have:
n = 23.7°
r = 22 ft
We need to find:
s
[tex] s = \dfrac{74.4}{360}2 \pi (22 ft) [/tex]
[tex] s = 9.1~ft [/tex]
