 # Find the radius of a circle in which the central​ angle, a , intercepts an arc of the given lengt Wade Bullock 2022-07-10 Answered
Find the radius of a circle in which the central​ angle, $a$, intercepts an arc of the given length s. Round to the nearest hundredth as needed.
$a=144,s=102$
The​ length, $s$, of an arc intercepted by a central angle of radians on a circle of radius $r$ is given by the formula below.
$s=ar$
This formula is only valid if a is measured in radians, so you must use the following formula to convert from degrees to radians.
$d\cdot \frac{\pi }{180}$
What I am confused about is that in the example guide that came along with the question, it gets $\frac{4\pi }{5}rad$ from the degree to radian conversion. How did they get to that answer?
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$144°=144×{\frac{\pi }{180}}^{c}={\frac{4\pi }{5}}^{c}.$ Here ${x}^{c}$ represents an angle of $x$ radians.