Question

A circle has a chord that goes from `( 5 pi)/8` to `(4 pi) / 3` radians on the circle. If the area of the circle is `16 pi`, what is the length of the chord?

Answer 1

`c ~~ 7.17`

Explanation:

Use the formula

`"Area" = pir^2`

to find the value of r:

`16pi = pir^2`

`r^2 = 16`

`r = 4`

The angle between two radii to each end of the chord is:

`theta = (4pi)/3-(5pi)/8`

`theta = (17pi)/24`

Because the two radii and the chord form a triangle we can use The Isosceles case of The Law of Cosines to find the length of the chord, c:

`c^2 = 2r^2(1-cos(theta))`

`c = sqrt(2(4)^2(1 - cos((17pi)/24)))`

`c ~~ 7.17`