Question

Points `(2 ,9 )` and `(1 ,5 )` are `(3 pi)/4` radians apart on a circle. What is the shortest arc length between the points?

Answer 1

The arc length is `=5.26`

Explanation:

The angle `theta=3/4pi`

The distance between the points is

`d=sqrt((2-1)^2+(9-5)^2)`

`=sqrt(1+16)`

`=sqrt17`

This is the length of the chord

So,

`d/2=rsin(theta/2)`

`r=d/(2sin(theta/2))`

`=sqrt17/(2sin(3/8pi))`

`=2.23`

The length of the arc is

`L=rtheta=2.23*3/4pi=5.26`