# A circle has a chord that goes from (2 pi)/3  to (5 pi) / 8  radians on the circle. If the area of the circle is 120 pi , what is the length of the chord?

Aug 7, 2016

$= 1.43$

#### Explanation:

A chord that goes from $2 \frac{\pi}{3}$to $5 \frac{\pi}{8}$
so it travels the distance $2 \frac{\pi}{3} - 5 \frac{\pi}{8} = \frac{\pi}{24}$;
or
$\frac{\pi}{24} \div 2 \pi = \frac{1}{48}$ of the Circumference of the Circle
Area of the Circle$= \pi {r}^{2} = 120 \pi$
or
${r}^{2} = 120$
or
$r = \sqrt{120}$
or
$r = 10.95$
Circumference of the circle$= 2 \pi r = 2 \left(\pi\right) \left(10.95\right) = 68.83$
Therefore Length of the chord$= 68.83 \left(\frac{1}{48}\right) = 1.43$