Question

A circle has a chord that goes from `pi/4` to `(5 pi) / 8` radians on the circle. If the area of the circle is `120 pi`, what is the length of the chord?

Answer 1

The length of the chord is: `c ~~ 12.17`

Explanation:

We are given the area of the circle:

`A = pir² = 120pi`

`r = sqrt120`

Because two radii and the chord form a triangle, we can use the law of cosines to find the length of the chord:

`c² = a² + b² - 2(a)(b)cos(C)`

where `a = b = r = sqrt120`, and `C = 5pi/8 - pi/4 = 3pi/8`

`c² = (sqrt120)² + (sqrt120)² - 2(sqrt120)(sqrt120)cos(3pi/8)`

`c ~~ 12.17`