0
$\begingroup$

(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.

$s=ar$

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?

$\endgroup$
1
  • $\begingroup$ 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
0
$\begingroup$

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.