# 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.

(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?

• Plug $144$ into $d$ but simplify it without using your calculator. You will find that both $144$ and $180$ have common factors. 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.