Question

Points `(6 ,2 )` and `(7 ,5 )` are `(2 pi)/3` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

Shortest arc length `s = R * theta = color(green)(3.8239`

Explanation:

Given `theta = (2pi)/3 = 120^0`#

`c = sqrt((7-6)^2 + (5-2)^2) = 3.1623`

`r = c / (2 sin ((2pi)/6)) = 3.1623 / (2 * sin 60) = 1.8258`

Shortest arc length `s = R * theta = 1.8258 * ((2pi) / 3) = color(green)3.8239`