(This is taken from a Pearson quiz)

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.


This formula is only valid if $a$ is measured in radians, so you must use the following formula to convert from degrees to radians.


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?

  • $\begingroup$ Plug $144$ into $d$ but simplify it without using your calculator. You will find that both $144$ and $180$ have common factors. $\endgroup$
    – John Douma
    May 22 at 21:10

$144°=144×\frac {\pi}{180} ^c=\frac {4\pi}{5}^c.$ Here $x^c$ represents an angle of $x$ radians.


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