Answer:
The first option is correct.
[tex]s=125.7 \ ft[/tex]
Step-by-step explanation:
The given problem is asking for the distance the handler travels the sector of a circle which is the arc length.
[tex]\boxed{\left\begin{array}{ccc}\text{\underline{Arc Length:}}\\\\s=r \theta \ \text{(In radians)}\\\\s=\frac{\theta}{180 \textdegree}\pi r \ \text{(In degrees)}\end{array}\right}[/tex]
Use the appropriate formula to find the arc length.
Given:
[tex]r=80 \ ft\\\theta= 90 \textdegree \ \text{in degrees or} \ \frac{\pi}{2} \ \text{in radians} \ \text{(Quarter circle)}[/tex]
We can use either formula according to your preference as long as you input the appropriate value. a degree angle would go into the degree formula and a radian angle would go into the radian formula. I will use both formulas just to prove to you they both work.
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In degrees:
[tex]s=\frac{\theta}{180 \textdegree}\pi r\\\\\Longrightarrow s=\frac{90 \textdegree}{180 \textdegree}\pi (80 \ ft)\\\\\Longrightarrow s=\frac{1}{2}\pi (80 \ ft)\\\\\Longrightarrow s=40 \pi \ ft\\\\\therefore \boxed{\boxed{s=125.664 \ ft}}[/tex]
In radians:
[tex]s=r \theta\\\\\Longrightarrow s=(80 \ ft)(\frac{\pi}{2} )\\\\\Longrightarrow s=40\pi \ ft\\\\\therefore \boxed{\boxed{s=125.664 \ ft}}[/tex]
Thus, the distance the handler travels is found. Quick Note: The first option's rounding is off by 0.1, but this is the closest to the answer.
