the area of the shaded sector is 8π. what is the measure of ∠sot, which corresponds to the minor arc st? a 34° b 45° c 48° d 50°

Question

Accepted Answer

# Answer:
B. $45^\circ$
# Explanation:
## Step1: Recall the formula for the area of a sector
The formula for the area of a sector of a circle with radius $r$ and central angle $\theta$ (in degrees) is $A=\frac{\theta}{360^\circ}\times\pi r^{2}$.
## Step2: Identify the given values
We know that the area of the sector $A = 8\pi$ and the radius $r = 8$.
## Step3: Substitute the values into the formula and solve for $\theta$
Substitute $A = 8\pi$ and $r = 8$ into the formula $A=\frac{\theta}{360^\circ}\times\pi r^{2}$:
$$
\begin{align*}
8\pi&=\frac{\theta}{360^\circ}\times\pi\times(8)^{2}\
8\pi&=\frac{\theta}{360^\circ}\times64\pi\
\end{align*}
$$
Divide both sides by $\pi$:
$$
8=\frac{\theta}{360^\circ}\times64
$$
Then, solve for $\theta$:
$$
\begin{align*}
\frac{\theta}{360^\circ}&=\frac{8}{64}\
\frac{\theta}{360^\circ}&=\frac{1}{8}\
\theta&=\frac{360^\circ}{8}\
\theta& = 45^\circ
\end{align*}
$$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Identify the given values

Step3: Substitute the values into the formula and solve for \(\theta\)

Answer: