Question

Find the radius of a circle in which a 62.8° central angle cuts off an arc length of 18.4 centimeters.

Answer 1

radius=17.22 centimeters

Explanation

we can use the formula for length of an arc

$l=2\pi\text{ r }(\frac{\Theta}{360})$

where l is the length of the arc, r is the radius, and theta is the angle in degrees

then

Let

$\begin{gathered} \Theta=62.8\~ \\ l=18.4 \end{gathered}$

now, replace

$\begin{gathered} l=2\pi\text{ r }(\frac{\Theta}{360}) \\ l=2\pi\text{ r }(\frac{62.8}{360}) \\ 18.4=2\pi r(0.17444) \\ 18.4=0.34\text{ }\pi\text{ r} \\ \text{divide both sides by 0.34 }\pi \\ \frac{18.4}{0.34\pi}=\frac{0.34\text{ }\pi\text{ r}}{0.34\pi} \\ 17.22=\text{radius} \end{gathered}$

I hope this helps you