in circle h with ( mangle ghj = 54^{circ} ) and ( gh = 17 ), find the area of sector ghj. round to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Recall the formula for the area of a sector
The formula for the area of a sector of a circle is $A=\frac{\theta}{360}\times\pi r^{2}$, where $\theta$ is the central angle in degrees and $r$ is the radius of the circle.
## Step2: Identify the values of $\theta$ and $r$
Given that $\theta = 54^{\circ}$ and $r = GH=17$.
## Step3: Substitute the values into the formula
$$
\begin{align*}
A&=\frac{54}{360}\times\pi\times(17)^{2}\
&=\frac{3}{20}\times\pi\times289\
&=\frac{867\pi}{20}
\end{align*}
$$
## Step4: Calculate the numerical value
$$
\begin{align*}
A&=\frac{867\times3.14159}{20}\
&=\frac{2723.75853}{20}\
& = 136.19
\end{align*}
$$

# Answer:
$136.19$

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the formula for the area of a sector

Step2: Identify the values of \(\theta\) and \(r\)

Step3: Substitute the values into the formula

Step4: Calculate the numerical value

Answer: