Question

A circle's center is at `(3 ,9 )` and it passes through `(5 ,8 )`. What is the length of an arc covering `(5pi ) /4` radians on the circle?

Answer 1

`=8.8`

Explanation:

Distance between the points `(3,9)` and `(5,8)` is Radius(`r`) of the Circle.
Distance or Radius(`r`)
`=sqrt((5-3)^2+(9-8)^2`
`=sqrt((2)^2+1^2)`
`=sqrt(4+1)`
`=sqrt5`
`=2.24`
Circumference of the Circle `=2pir=2pi(2.24)=14.07`
Arc covers `(5pi)/4` radians of the Circle
or
Arc covers `(5pi)/4-:2pi=5/8`th Circumference of the Circle
Length of the arc `=5/8(14.07)=8.8`