Question

hi can someone plz help me solve this? i have my math exam in 2 hourS and cannot find the answer anywher ...... A sector of a circle of radius 12 miles has an area of 72 square miles.
Find the central angle of this sector in degrees.

Answer 1

\[\frac{x}{72}=\frac{2\pi}{144\pi}\]

Answer 2

so i just solve for x for the angle?

Answer 3

yes

Answer 4

the formula for the area of a sector is as follows:

\[(\Theta \div360)\times \pi(r)^{?}\]

so substituting the values would give

(Theta/360) x pi(12)^2 = 72

so (Theta/360) = 72/(pi(12)^2)

therefore

\[\theta = (72/\pi(12)^{2})\times360\]

gives you something like 57.3 degs

Answer 5

thanks really appreciate it :)