in circle g with ( mangle fgh = 110^{circ} ) and ( fg = 6 ) units, find the length of ( overparen{fh} ). round to the nearest hundredth.

Question

Accepted Answer

# Explanation:
## Step1: Recall the arc - length formula
The formula for the length of an arc $l$ is $l=\frac{n\pi r}{180}$, where $n$ is the central angle and $r$ is the radius of the circle.
## Step2: Identify the values of $n$ and $r$
Given that $n = m\angle FGH=110^{\circ}$ and $r = FG = 6$ units.
## Step3: Substitute the values into the formula
Substitute $n = 110$ and $r = 6$ into $l=\frac{n\pi r}{180}$.
$$
\begin{align*}
l&=\frac{110\times\pi\times6}{180}\
&=\frac{660\pi}{180}\
&=\frac{11\pi}{3}
\end{align*}
$$
## Step4: Calculate the numerical value
Using $\pi\approx3.14159$, we have $l=\frac{11\times3.14159}{3}\approx11.52$

# Answer:
$11.52$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Recall the arc - length formula

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

Step3: Substitute the values into the formula

Step4: Calculate the numerical value

Answer: