A circle's center is at (2 ,4 ) and it passes through (3 ,1 ). What is the length of an arc covering (15pi ) /8 radians on the circle?

1 Answer
Aug 11, 2016

=18.75

Explanation:

Circle's center is at (2,4) and it passes through (3,1)
Therefore Length of the radius=r =Distance between these points(2,4) and (3,1)
or
radius =r=sqrt((3-2)^2+(4-1)^2)
=sqrt(1^2+3^2)
=sqrt(1+9)
=sqrt10
=3.16
Therefore Circumfernce of the Circle =2pir=2pitimes3.16~=20
Arc covers (15pi)/8 radians on the Circle
In other words Arc covers (15pi)/8-:2pi=15/16times (circumference of the Circle)
Therefore Length of the Arc =15/16 times2pir=15/16 times20=18.75